de.wikipedia.org website review
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de.wikipedia.org is 60% geoptimaliseerd!
SEO Keyword summary for de.wikipedia.org/wiki/quadratwurzel
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle der sqrt |
long Tail Keywords (2 words) reellen zahlen ydisplaystyle y quadratwurzeln aus der quadratwurzelfunktion aus reellen |
long Tail Keywords (3 words) ydisplaystyle y ist zahl ydisplaystyle y ydisplaystyle sqrt y aus reellen zahlen fr die quadratwurzel quadratwurzeln aus reellen berechnung fr den |
de.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a de.wikipedia.org/wiki/quadratwurzel page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
quadratwurzel ndash wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
displaystyle ysqrt sqrt yfrac cdot geq ygeq xcdot beginalignedqcolon infty rightarrow xmapsto endaligned ymapsto xsqrt mathbb acdot bsqrt leq aleq bleq ablongleftrightarrow asqrt frac mathrm xmathrm xfrac fxtfrac beginarrayccccrsqrt approx endarray tmapsto sum binom nxnsum nnfrac nxn dotsb xleq tleq aoverline rtfrac abc overline textstyle zrcdot varphi rcdot qcolon zmapsto dmathrm yin mid text oder und zxmathrm zsqrt tfrac operatorname sgn ycdot ybegincases endcases zzcdot argz argzin zmathrm angle eoz zxy ein zweig der quadratwurzel zweiter die riemannsche flche lsst erkennen wie beiden zweige ineinander bergehen zleft rightsqrt beginalignedw emsqrt lefttfrac rightendaligned right brarcdot brqquad qquad quad textp abin abz leftsqrt zright arg argsqrt nmathbb equiv xbmod dotsm pkmk not bmod pmathbb leftfrac xprightequiv xprightbegincases textwenn xtext quadratischer nichtrest modulo ptext ist nicht teilerfremd sind rest istendcases bigl xpbigr qequiv rleftwfrac wfrac rightbmod xpright wnbegincasesr wenn ntext geradewn ungeradeendcases rleftw beginmatrixw endmatrix rightequiv abcdot bleftrightarrow btext wurzel von afrac ggigxi xiidelta dotsc ffifxi gfi gfibeginpmatrixg endpmatrixbeginpmatrixf endpmatrixbeginpmatrixdelta xdelta delta xendpmatrix hhihxi hgifiifi beginpmatrixdelta ibeta beginpmatrixalpha alpha endpmatrix xbeta ksum kfrac gamma beta kjgamma llilxi lfibeta beginpmatrixl endpmatrixbeginpmatrixalpha ifrac wikimedia foundation powered mediawiki
Mobile SEO de.wikipedia.org/wiki/quadratwurzel
Mobile rendering
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Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
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Marketing / lead generation for de.wikipedia.org/wiki/quadratwurzel
Social Media
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Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
quadratwurzel found in path !
wurzel found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
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Favicon icon found?
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Robots.txt found?
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Sitemap found?
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Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistiken
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versionsgeschichte
seiteninformationen
druckversion
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wiki doppeltlogarithmischer darstellung
steigung
englisch
quadrat
wurzelzeichen
term
potenzgesetz
gleichung
lsungen
rationale zahlen
antike
euklids beweis der irrationalitt der wurzel aus 2
symbol
16jahrhunderts
r
carl friedrich gau
programmiersprachen
reellen zahl
umkehrfunktion
injektiv
surjektiv
beweis der irrationalitt der wurzel aus 2 bei euklid
betrag
differenzierbar
abgeschlossenen teilintervall
definitionsbereichs
riemannintegrierbar
stammfunktionen
natrlichen zahl
irrationale zahl
dezimalbruchentwicklung
schriftliches wurzelziehen
algorithmus
intervallschachtelung
babylonisches wurzelziehen
iterationsverfahren
taschenrechner
konvergiert
newtonverfahren
taylorreihen
binomische reihe
konvergiert
cordic
fpus
mikrocontrollern
faktoren
division
konstruktion mit zirkel und lineal
produkt
kathetensatz
zahlengeraden
thaleskreis
senkrechte
rechtwinkligen dreiecks
hhensatz
geraden
subtraktion
addition
geometrischen mittels
winkelhalbierenden
strahlen
punktspiegelung
komplexen zahlenebene
bijektive
kartesischen koordinaten
vorzeichenfunktion
polarkoordinaten
punktspiegelung
ursprung
riemannsche flche
identitt
restklassenring
primfaktorzerlegung
chinesischen restsatzes
primzahlen
legendresymbols
quadratwurzel einer matrix
matrix
positiv definite
symmetrische
spektralsatz
choleskyzerlegung
exponentialabbildung
diffeomorphismus
matrizenmultiplikation
wurzel aus 2
euklids beweis fr irrationalitt von wurzel2
wurzel aus 3
wurzel mathematik
modulo
quadratwurzelgesetz von penrose
lesen
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Links to external pages
Outloing links
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SEO Advice for de.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 43% | A title should reflect the contents of a site. This site has a 33 % match | |
Title Length | 80% | Limit your title to anywhere between 40 and 70 characters. Your title was 32 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 70% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 148 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 5 folders above or in the first level of navigation. | |
Headings | 53% | Headers should reflect the contents of a site. This site has a 23 % match | |
Links | 12% | Link anchors should to some degree reflect the contents of a site. This site has a 6 % match | |
Image alt tags | 34% | Image alt tags should to some degree reflect the contents of a site. This site has a 12 % match | |
Bold and italic | 90% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 30 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 96% | 95.819935691318 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 5109 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 73.97% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 618 inline style declarations ( <a style="color:green">) with a size of 21461 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (3) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 100% | Perfect, we found a correct use of normalized headings ! |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
de.wikipedia.org images and descriptions
209 images found at de.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c1f2c2437bae14145e43c54cb7e1ee2701b2106 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} _{+}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61a85116427b03fe133dcfd6bd6e35052364654b height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{ccccr}{\sqrt {2}}&\approx &{\sqrt {\frac {49}{25}}}&=&{\frac {7}{5}}\\{\sqrt {2}}&\approx &{\sqrt {\frac {289}{144}}}&=&{\frac {17}{12}}\\{\sqrt {2}}&\approx &{\sqrt {\frac {1681}{841}}}&=&{\frac {41}{29}}\\{\sqrt {3}}&\approx &{\sqrt {\frac {49}{16}}}&=&{\frac {7}{4}}\\{\sqrt {3}}&\approx &{\sqrt {\frac {361}{121}}}&=&{\frac {19}{11}}\\{\sqrt {5}}&\approx &{\sqrt {\frac {81}{16}}}&=&{\frac {9}{4}}\\{\sqrt {6}}&\approx &{\sqrt {\frac {2401}{400}}}&=&{\frac {49}{20}}\\{\sqrt {7}}&\approx &{\sqrt {\frac {64}{9}}}&=&{\frac {8}{3}}\\{\sqrt {8}}&\approx &{\sqrt {\frac {289}{36}}}&=&{\frac {17}{6}}\\{\sqrt {10}}&\approx &{\sqrt {\frac {361}{36}}}&=&{\frac {19}{6}}\\{\sqrt {11}}&\approx &{\sqrt {\frac {100}{9}}}&=&{\frac {10}{3}}\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/53a903aaa51d4d5f19df46c05c75eff18688a1a6 height: height attribute not set width: width attribute not set description: {\displaystyle 1{,}4^{2}=1{,}96<2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc193caf6bee875192277893a0c663e0eea14bc7 height: height attribute not set width: width attribute not set description: {\displaystyle 1{,}5^{2}=2{,}25>2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dcfba22d0c90c2c961e8a972a36e2e4aa6492d10 height: height attribute not set width: width attribute not set description: {\displaystyle 1{,}41421356^{2}<2<1{,}41421357^{2}\;\rightarrow \;{\sqrt {2}}\approx 1{,}41421356} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87c05e162526a543ec66ddc69710d91933038524 height: height attribute not set width: width attribute not set description: {\displaystyle x\mapsto x^{2}-a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5df932f5210d9d4c2e1b4df2196eaf937f2ed4b2 height: height attribute not set width: width attribute not set description: {\displaystyle t\mapsto {\sqrt {t}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/970dea4a5f5ec5355c4cdd62f6396fbc8b1baaa1 height: height attribute not set width: width attribute not set description: {\displaystyle t=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/133a92bcd75133933abf89509bdfa8bb942de139 height: height attribute not set width: width attribute not set description: {\displaystyle x\mapsto (1+x)^{1/2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e55a9d7782833cc210d5e78d49b12d6f1d63c48 height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{n=0}^{\infty }{\binom {1/2}{n}}\,x^{n}=\sum _{n=0}^{\infty }{\binom {2n}{n}}\,{\frac {(-1)^{n+1}}{(2n-1)\,4^{n}}}\,x^{n}=1+{\frac {1}{2}}x-{\frac {1}{8}}x^{2}+{\frac {1}{16}}x^{3}-{\frac {5}{128}}x^{4}\pm \dotsb } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad95e9e3840f09ecffbe53c104ee1bbf639fd42 height: height attribute not set width: width attribute not set description: {\displaystyle |x|\leq 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8b52f282420b9d2b6625eb1889455838334976f height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {1+x}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/452a9c7d7a985d6cf5e94238b5c36a589dd012f2 height: height attribute not set width: width attribute not set description: {\displaystyle x:=t-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95b864ee4a32a5d22e6f5919cb5c5689f3ede230 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {t}}=1+{\frac {1}{2}}(t-1)-{\frac {1}{8}}(t-1)^{2}+{\frac {1}{16}}(t-1)^{3}-{\frac {5}{128}}(t-1)^{4}\pm \dotsb } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/49ccf5f027b2f02f8baeb0483b96ac32b78e053c height: height attribute not set width: width attribute not set description: {\displaystyle 0\leq t\leq 2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf height: height attribute not set width: width attribute not set description: {\displaystyle 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc5b9d9fb0ff9d4455e75ccd29676bd7f33da80e height: height attribute not set width: width attribute not set description: {\displaystyle a>1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950 height: height attribute not set width: width attribute not set description: {\displaystyle 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ec6716e83bd51c36e9dbb6a16fa69e07c732a292 height: height attribute not set width: width attribute not set description: {\displaystyle a={\overline {ab}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01f0231f67615b09e15198bb91c56b0394eaa8cf height: height attribute not set width: width attribute not set description: {\displaystyle r={\tfrac {a}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029 height: height attribute not set width: width attribute not set description: {\displaystyle c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e55b44cfd965fbdc7a328d5db8a35a619db0971 height: height attribute not set width: width attribute not set description: {\displaystyle abc} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/998c74ac292731e915ab6f448f008194c107c4a4 height: height attribute not set width: width attribute not set description: {\displaystyle 1+a} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/01-quadratwurzel_gr%c3%b6%c3%9fer_1.svg/240px-01-quadratwurzel_gr%c3%b6%c3%9fer_1.svg.png height: 129 width: 240 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/wurzelkonstruktion_mit_hoehensatz.svg/200px-wurzelkonstruktion_mit_hoehensatz.svg.png height: 129 width: 200 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f4/01-quadratwurzel_kleiner_1.svg/240px-01-quadratwurzel_kleiner_1.svg.png height: 129 width: 240 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8d3f65a187e46328021b646ee8769425a04d72 height: height attribute not set width: width attribute not set description: {\displaystyle a<1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8028f23cfdcb108712e2bc53369305574afe820b height: height attribute not set width: width attribute not set description: {\displaystyle a+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/075d661417b8ca5a991a2a7bd4991cc1ab856d9d height: height attribute not set width: width attribute not set description: {\displaystyle b,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a1fc1e5d1cc3234643a7eaec30868a5b5eea9504 height: height attribute not set width: width attribute not set description: {\displaystyle a1c} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/01_construction_of_square_root_of_product-2.svg/240px-01_construction_of_square_root_of_product-2.svg.png height: 127 width: 240 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/fc/01_construction_of_square_root_of_product-1.svg/239px-01_construction_of_square_root_of_product-1.svg.png height: 127 width: 239 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3 height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/39d81124420a058a7474dfeda48228fb6ee1e253 height: height attribute not set width: width attribute not set description: {\displaystyle 6} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/295b4bf1de7cd3500e740e0f4f0635db22d87b42 height: height attribute not set width: width attribute not set description: {\displaystyle 4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/92fdeed4d94de5ea7387d67e20b1dd1929433c7b height: height attribute not set width: width attribute not set description: {\displaystyle {\overline {0\;10}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f8f75bd44bad129d6b7627f3ff8092d13c53492 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {24}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/addc8519724f81b43a6883c5eb2c996f9fc2996f height: height attribute not set width: width attribute not set description: {\displaystyle -4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f height: height attribute not set width: width attribute not set description: {\displaystyle 2} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/imaginary2root.svg/220px-imaginary2root.svg.png height: 220 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a401847d69a1352834e66e970a2e8867f7425851 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {\mathrm {i} }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98 height: height attribute not set width: width attribute not set description: {\displaystyle z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e5a953292d49e530fb8ab87db8adff44bae46a2b height: height attribute not set width: width attribute not set description: {\displaystyle w^{2}=z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6 height: height attribute not set width: width attribute not set description: {\displaystyle w} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/876c2a24ff0760e6f5827a437646049f9d0134cb height: height attribute not set width: width attribute not set description: {\textstyle {\sqrt {|z|}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7764453a30766108f395920e29d6b644c058134d height: height attribute not set width: width attribute not set description: {\displaystyle z=r\cdot \mathrm {e} ^{\mathrm {i} \varphi },} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e height: height attribute not set width: width attribute not set description: {\displaystyle \varphi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23cbbcd53bd13620bc53490e3eec42790850b452 height: height attribute not set width: width attribute not set description: {\displaystyle r>0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b27eb4930922e649015e37b8d782b6b1ad7d55b9 height: height attribute not set width: width attribute not set description: {\displaystyle -\pi <\varphi \leq \pi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/51b9a30cc778c9bd895364f0739ae230f3f698f3 height: height attribute not set width: width attribute not set description: {\displaystyle w_{1}={\sqrt {r}}\cdot \mathrm {e} ^{\mathrm {i} \varphi /2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0705b6e9060a8d13405837650df9da20cdecf5e7 height: height attribute not set width: width attribute not set description: {\displaystyle w_{2}={\sqrt {r}}\cdot \mathrm {e} ^{\mathrm {i} (\varphi /2+\pi )}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3722346f8c6b4f454e0437e447a06e8635585d72 height: height attribute not set width: width attribute not set description: {\displaystyle q\colon \mathbb {c} \rightarrow \mathbb {c} ;z\mapsto z^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f34a0c600395e5d4345287e21fb26efd386990e6 height: height attribute not set width: width attribute not set description: {\displaystyle d} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e727d80c47b394d4cb9b713437a11b8119f5d9a height: height attribute not set width: width attribute not set description: {\displaystyle d_{\mathrm {h} }:=\{x+\mathrm {i} \,y\in \mathbb {c} \mid x>0{\text{ oder }}(x=0{\text{ und }}y\geq 0)\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6f54decce2770122b2b246ef06aa6acb003afcce height: height attribute not set width: width attribute not set description: {\displaystyle d_{\mathrm {h} }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a681c3407545aa71422f71b09d2ec10d1ad116a3 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {z}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f034e7d7b0ff90492fb520f9af4687b508f8e9d height: height attribute not set width: width attribute not set description: {\displaystyle z=x+\mathrm {i} y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5bbae71a4b8eb54c4463dafdde6e8b13084f17e0 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {z}}={\sqrt {x+\mathrm {i} y}}={\sqrt {\tfrac {|z|+x}{2}}}+\mathrm {i} \cdot \operatorname {sgn^{+}} (y)\cdot {\sqrt {\tfrac {|z|-x}{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ce4916c3fe1c3235ab5cd8fce6ff6249f2100be3 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {sgn^{+}} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/094f824655138f6b11d96a0da32e7f0716ba6959 height: height attribute not set width: width attribute not set description: {\displaystyle y=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ec838dfd8a4a659b2877f93a6b53f22fc7777d07 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {sgn} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8000bee5a2d00f863975f0012769b8004e4641 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {sgn} ^{+}(y)={\begin{cases}+1&{\text{ für }}y\geq 0\\-1&{\text{ für }}y<0\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ea5f443cd213f518fbefee8adf17aeeeb8a63aa0 height: height attribute not set width: width attribute not set description: {\displaystyle -{\sqrt {z}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c3de8d555d78005f6335c678716cccaa46572ac3 height: height attribute not set width: width attribute not set description: {\displaystyle z=|z|\cdot \mathrm {e} ^{\mathrm {i} \cdot \arg(z)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b49f881e0c5973f5c7738a22d3b33b9a21d78558 height: height attribute not set width: width attribute not set description: {\displaystyle \arg(z)\in (-\pi ,\pi ]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee0ac5e2eeeda105282afa814114b5fd861a14e0 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {z}}={\sqrt {|z|}}\mathrm {e} ^{\mathrm {i} \cdot \arg(z)/2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28fd4d7dcabf618d707c21bd08306c7b3aa8b68e height: height attribute not set width: width attribute not set description: {\displaystyle |z|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/519e03ebf03039d1b82a259be4d14269388278e5 height: height attribute not set width: width attribute not set description: {\displaystyle -{\sqrt {z}}={\sqrt {|z|}}\mathrm {e} ^{\mathrm {i} \cdot (\arg(z)/2+\pi )}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d8bb9d3cf9c1a82f1666e4e72b6702b0cee4b21 height: height attribute not set width: width attribute not set description: {\displaystyle \arg(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1b231e8ae9bbdc4e3294a4675c9d77b0f29c17a8 height: height attribute not set width: width attribute not set description: {\displaystyle z=x+\mathrm {i} \,y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c397c0781d0a8556e6fb169b7ccd7bf7eade63f5 height: height attribute not set width: width attribute not set description: {\displaystyle \angle (eoz)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5dbd91429699c0f03884dd4d74057420a38b9a6 height: height attribute not set width: width attribute not set description: {\displaystyle e(1|0),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81df91cc1cac32e832b48edc90ae32a3d985a955 height: height attribute not set width: width attribute not set description: {\displaystyle o(0|0)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/13bf693f37753a7b8e619c5d34d0e925820b5964 height: height attribute not set width: width attribute not set description: {\displaystyle z(x|y)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f6728d2b30f42f88b52281be5ae0584fdc9df64 height: height attribute not set width: width attribute not set description: {\displaystyle w_{1}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e2/complex_sqrt_leaf1.jpg/200px-complex_sqrt_leaf1.jpg height: 200 width: 200 description: ein zweig der quadratwurzel |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f6/complex_sqrt_leaf2.jpg/200px-complex_sqrt_leaf2.jpg height: 200 width: 200 description: zweiter zweig |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/riemann_surface_sqrt.svg/190px-riemann_surface_sqrt.svg.png height: 200 width: 190 description: die riemannsche fläche der quadratwurzel lässt erkennen, wie die beiden zweige ineinander übergehen. |
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https://upload.wikimedia.org/wikipedia/commons/0/06/bsp_quadratwurzel_c.png height: 250 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95b621bef5d6a76f135f3f9f37f67251c1dda564 height: height attribute not set width: width attribute not set description: {\displaystyle z=-1+\mathrm {i} \,{\sqrt {3}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d6c699b7e9f6ec3eff991163d8359d91b9cbc1d height: height attribute not set width: width attribute not set description: {\displaystyle |z|=\left|-1+\mathrm {i} {\sqrt {3}}\right|={\sqrt {(-1)^{2}+({\sqrt {3}})^{2}}}={\sqrt {1+3}}={\sqrt {4}}=2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c65fbfa85729505faa6fa18dff479108b517c08c height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}w_{1}&={\sqrt {\tfrac {2+(-1)}{2}}}+\mathrm {i} \cdot \operatorname {sgn^{+}} ({\sqrt {3}})\cdot {\sqrt {\tfrac {2-(-1)}{2}}}\\[0.3em]&={\sqrt {\tfrac {1}{2}}}+\mathrm {i} \cdot (+1)\cdot {\sqrt {\tfrac {3}{2}}}={\sqrt {2}}\cdot \left({\tfrac {1}{2}}+\mathrm {i} \cdot {\tfrac {1}{2}}{\sqrt {3}}\right)\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/562ff35b4484b54f67a88fcb4e390d914d109fc4 height: height attribute not set width: width attribute not set description: {\displaystyle w_{2}=-w_{1}={\sqrt {2}}\cdot \left(-{\tfrac {1}{2}}-\mathrm {i} \cdot {\tfrac {1}{2}}{\sqrt {3}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/df0a2c6f2ec35d147ab6fceadbc63d535303d227 height: height attribute not set width: width attribute not set description: {\displaystyle (a\cdot b)^{r}=a^{r}\cdot b^{r}\qquad \qquad \qquad \qquad \qquad \qquad \quad {\text{(p)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10be37badc90b3dbaaab886a4a4a76c6f1694869 height: height attribute not set width: width attribute not set description: {\displaystyle r=1/2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/084d8fe36677ad2f908acc909b6ff59d9e9964dc height: height attribute not set width: width attribute not set description: {\displaystyle a,b\in \mathbb {c} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47a41a42ca3ca59e45897640e0cadd9903508b51 height: height attribute not set width: width attribute not set description: {\displaystyle a=b=:z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3343ab37e1e971da1d89dd83f35c87c9077de72c height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {z^{2}}}=\left({\sqrt {z}}\right)^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3013a1f7c46516fb5c5992cb8c894fdeec455ce8 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\sqrt {z}}\right)^{2}=z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a49528d16d65f3056b04e804406b820791d3d55 height: height attribute not set width: width attribute not set description: {\displaystyle {\sqrt {z^{2}}}=z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af5d92c041c1ddaa688b8f7f68d333e107e93709 height: height attribute not set width: width attribute not set description: {\displaystyle z=-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1b0dc632f669ba5bebd0626878471178e3e981c2 height: height attribute not set width: width attribute not set description: {\displaystyle (-1)^{2}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9db438212ce8598dbc2c11604415331b9030fd38 height: height attribute not set width: width attribute not set description: {\displaystyle \arg(1)=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ed86cebfa33e73893f16a5539a227098b98afe9 height: height attribute not set width: width attribute not set description: {\textstyle {\sqrt {(-1)^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/408cdf5b533dc8240f01d911accb6e4808b2e2bd height: height attribute not set width: width attribute not set description: {\textstyle \arg({\sqrt {1}})=0/2=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/704fb0427140d054dd267925495e78164fee9aac height: height attribute not set width: width attribute not set description: {\displaystyle -1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61ff564e0c96a860b835af43294cfa4fcca159e8 height: height attribute not set width: width attribute not set description: {\displaystyle \arg(-1)=\pi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee2e91479ebcbf4f3f96daa1fb07bf6728ef65f7 height: height attribute not set width: width attribute not set description: {\displaystyle {\text{(p)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f2120ebbc85f91df66c6de5446367bf9fd620844 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {z} /n\mathbb {z} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b7209f3cefe439d24e416824a4c8a54a8b6abc00 height: height attribute not set width: width attribute not set description: {\displaystyle q^{2}\equiv x{\bmod {n}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84bd8ef6df9d2b85176c0f46c86809fabb76eb5b height: height attribute not set width: width attribute not set description: {\displaystyle n=p_{1}^{m_{1}}\cdot p_{2}^{m_{2}}\dotsm p_{k}^{m_{k}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3bab32900e0cbcdf2743e43f83431e87e56c734e height: height attribute not set width: width attribute not set description: {\displaystyle p^{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d62e4100b94c1939c67f2d4b8580d26c78106c44 height: height attribute not set width: width attribute not set description: {\displaystyle p=2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2cbea824b174a0b068fd3422bc0a37f28c082908 height: height attribute not set width: width attribute not set description: {\displaystyle 0^{2}=0,\,1^{2}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84844ef7126acfff842afed3413f87f42c63a011 height: height attribute not set width: width attribute not set description: {\displaystyle 1\not \equiv 0{\bmod {2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36 height: height attribute not set width: width attribute not set description: {\displaystyle p} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/57869a3a3c4c431cc49c4c7ab1d9c7ea692b517b height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {z} /p\mathbb {z} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d0b48e06d988ee2874afc4696c8c11e3a779b249 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {x}{p}}\right)\equiv x^{\frac {p-1}{2}}{\bmod {p}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/138984ea00257c65034cdca76332adbf1ea514ae height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {x}{p}}\right)={\begin{cases}-1,&{\text{wenn }}x{\text{ quadratischer nichtrest modulo }}p{\text{ ist}}\\0,&{\text{wenn }}x{\text{ und }}p{\text{ nicht teilerfremd sind }}\\1,&{\text{wenn }}x{\text{ ein quadratischer rest modulo }}p{\text{ ist}}\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ef334ffba2f1fe81b292c3f1216c5574c19f13d height: height attribute not set width: width attribute not set description: {\displaystyle {\bigl (}{\tfrac {x}{p}}{\bigr )}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d68054c5a400a573e8fc67a4352e2ef2aaee44f9 height: height attribute not set width: width attribute not set description: {\displaystyle {\bigl (}{\tfrac {x}{p}}{\bigr )}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/efcc0ade18eb4148444dfa448beb57d4fcbfe4ca height: height attribute not set width: width attribute not set description: {\displaystyle q\equiv \pm x^{\frac {p+1}{4}}{\bmod {p}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/56783458a1fee52da208279b50350559791d34dc height: height attribute not set width: width attribute not set description: {\displaystyle q\equiv \pm {\frac {x}{2r}}\left(w_{\frac {p-1}{4}}+w_{\frac {p+3}{4}}\right){\bmod {p}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0445bac4753a0a316548630820f9543d26f2fa height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {r^{2}-4x}{p}}\right)=-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0fa0340872ef1d6511eaf27ed7c57f98589a693d height: height attribute not set width: width attribute not set description: {\displaystyle w_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/232a40f640856b67d05d8736a8d76b447af80624 height: height attribute not set width: width attribute not set description: {\displaystyle w_{n}={\begin{cases}r^{2}/x-2,&{\text{ wenn }}n=1\\w_{n/2}^{2}-2,&{\text{ wenn }}n{\text{ gerade}}\\w_{(n+1)/2}w_{(n-1)/2}-w_{1},&{\text{ wenn }}n>1{\text{ ungerade}}\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/871a5063af170fa536b144fbcc5745146a42cc13 height: height attribute not set width: width attribute not set description: {\displaystyle x=3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4c16c3c6ea81024b27e5d4dfc214442cb0d09673 height: height attribute not set width: width attribute not set description: {\displaystyle p=37} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23ff4f89435d662737301d72ebfe33749e46ba8a height: height attribute not set width: width attribute not set description: {\displaystyle q\equiv \pm {\frac {x}{2r}}\left(w_{9}+w_{10}\right){\bmod {3}}7} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c19b110d7eb52a69381b88554e63c8a2aef376c7 height: height attribute not set width: width attribute not set description: {\displaystyle r=2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f873124fc480240f6ac4a4ec155359b4f789fb71 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {r^{2}-4x}{p}}\right)\equiv (r^{2}-4x)^{\frac {p-1}{2}}\equiv (-8)^{18}\equiv 36\equiv -1{\bmod {3}}7} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9cb3934edfce27104cbbbb771f7c37beb8088739 height: height attribute not set width: width attribute not set description: {\displaystyle w_{9}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26dbefa8ca93a9be943b422a8e925866194fd376 height: height attribute not set width: width attribute not set description: {\displaystyle w_{10}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ae9e235816ddce5a7066c3952d005fb736f41a6b height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{matrix}w_{1}&\equiv &r^{2}/x-2&\equiv &4/3-2&\equiv &24&{\bmod {3}}7\\w_{2}&\equiv &w_{1}^{2}-2&\equiv &24^{2}-2&\equiv &19&{\bmod {3}}7\\w_{3}&\equiv &w_{1}w_{2}-w_{1}&\equiv &24\cdot 19-24&\equiv &25&{\bmod {3}}7\\w_{4}&\equiv &w_{2}^{2}-2&\equiv &19^{2}-2&\equiv &26&{\bmod {3}}7\\w_{5}&\equiv &w_{2}w_{3}-w_{1}&\equiv &19\cdot 25-24&\equiv &7&{\bmod {3}}7\\w_{9}&\equiv &w_{4}w_{5}-w_{1}&\equiv &26\cdot 7-24&\equiv &10&{\bmod {3}}7\\w_{10}&\equiv &w_{5}^{2}-2&\equiv &7^{2}-2&\equiv &10&{\bmod {3}}7\\\end{matrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/640438ccc3b2b0f2eee9459485635d67e091df53 height: height attribute not set width: width attribute not set description: {\displaystyle q\equiv \pm {\frac {x}{2r}}\left(w_{9}+w_{10}\right)\equiv \pm {\frac {3}{4}}(10+10)\equiv \pm 15{\bmod {3}}7.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f819aeee26beec95a5f0fe9debe6fb39d4af267 height: height attribute not set width: width attribute not set description: {\displaystyle a=b\cdot b\leftrightarrow b{\text{ ist wurzel von }}a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/adba896b74b0d7c0b3cb0dcf4c8db251829450fb height: height attribute not set width: width attribute not set description: {\displaystyle a^{\frac {1}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/21a064776b72c64c38d8fcb17e4afb67cf070d5c height: height attribute not set width: width attribute not set description: {\displaystyle g,\,g_{i}:=g(x_{i})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158 height: height attribute not set width: width attribute not set description: {\displaystyle x_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94309d7d6bf62d5f3333c7ff79d581fb5727a81c height: height attribute not set width: width attribute not set description: {\displaystyle x_{i}=i\delta x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95052b4574bf69a0b642b436ddc403c1586ea337 height: height attribute not set width: width attribute not set description: {\displaystyle i=0,1,\dotsc ,n-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25c033c9d3b3e6a90aa684b1909f7fee0c0d047c height: height attribute not set width: width attribute not set description: {\displaystyle f,\,f_{i}:=f(x_{i})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65da883ca3d16b461e46c94777b0d9c4aa010e79 height: height attribute not set width: width attribute not set description: {\displaystyle f_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95b3cd5db974f57f20390d76d8240d1a58e7105a height: height attribute not set width: width attribute not set description: {\displaystyle g=fi} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d928ec15aeef83aade867992ee473933adb6139d height: height attribute not set width: width attribute not set description: {\displaystyle n=4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/93ba622fe6e09d26e8b4bcecfafb4c43bb4b8275 height: height attribute not set width: width attribute not set description: {\displaystyle g=fi={\begin{pmatrix}g_{0}&g_{1}&g_{2}&g_{3}\\0&g_{0}&g_{1}&g_{2}\\0&0&g_{0}&g_{1}\\0&0&0&g_{0}\end{pmatrix}}={\begin{pmatrix}f_{0}&f_{1}&f_{2}&f_{3}\\0&f_{0}&f_{1}&f_{2}\\0&0&f_{0}&f_{1}\\0&0&0&f_{0}\end{pmatrix}}{\begin{pmatrix}\delta x&\delta x&\delta x&\delta x\\0&\delta x&\delta x&\delta x\\0&0&\delta x&\delta x\\0&0&0&\delta x\end{pmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc7ec0c355a8e1c3400258b8b865fb4a6b45b759 height: height attribute not set width: width attribute not set description: {\displaystyle h,\,h_{i}:=h(x_{i})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7cccbce4c46bd37d45172685f203e1e841e517e1 height: height attribute not set width: width attribute not set description: {\displaystyle h=gi=fii=fi^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f height: height attribute not set width: width attribute not set description: {\displaystyle i} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f7877295db09472492fb23a7716e7ce57462d0 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{pmatrix}\delta x&1&0&0\\0&\delta x&1&0\\0&0&\delta x&1\\0&0&0&\delta x\end{pmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1080bad15da8bd6c1860950995f7cd46e4afb6a height: height attribute not set width: width attribute not set description: {\displaystyle i^{\beta }={\begin{pmatrix}\alpha _{0}&\alpha _{1}&\alpha _{2}&\alpha _{3}\\0&\alpha _{0}&\alpha _{1}&\alpha _{2}\\0&0&\alpha _{0}&\alpha _{1}\\0&0&0&\alpha _{0}\end{pmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/11ff521355f6ff3eea5290d26f63843011c09ba2 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha _{0}=(\delta x)^{\beta }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a33a77f9bc65b2c6c07db72c4b03344e592500c7 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha _{k}=\sum _{j=1}^{k}{\frac {\gamma (\beta +1)(-1)^{j+1}\alpha _{k-j}}{\gamma (j+1)\gamma (\beta -j+1)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2b90b7fdfc4d34cb311e2e2bcec0a1b35caf0070 height: height attribute not set width: width attribute not set description: {\displaystyle k=1,2,\dotsc ,n-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8 height: height attribute not set width: width attribute not set description: {\displaystyle \beta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/edef8290613648790a8ac1a95c2fb7c3972aea2f height: height attribute not set width: width attribute not set description: {\displaystyle {\tfrac {1}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70 height: height attribute not set width: width attribute not set description: {\displaystyle \delta x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08f6a5a9d42e60c03bc514920969ca16327b820a height: height attribute not set width: width attribute not set description: {\displaystyle (\delta x)^{\frac {1}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/12f3ee946d7e981ff6f53ff7bccb32fdb6b0998e height: height attribute not set width: width attribute not set description: {\displaystyle l,\,l_{i}:=l(x_{i})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074 height: height attribute not set width: width attribute not set description: {\displaystyle f(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f7e69749767ca05926f82bcd183c7c7a82a82b1a height: height attribute not set width: width attribute not set description: {\displaystyle l=fi^{\beta }={\begin{pmatrix}l_{0}&l_{1}&l_{2}&l_{3}\\0&l_{0}&l_{1}&l_{2}\\0&0&l_{0}&l_{1}\\0&0&0&l_{0}\end{pmatrix}}={\begin{pmatrix}f_{0}&f_{1}&f_{2}&f_{3}\\0&f_{0}&f_{1}&f_{2}\\0&0&f_{0}&f_{1}\\0&0&0&f_{0}\end{pmatrix}}{\begin{pmatrix}\alpha _{0}&\alpha _{1}&\alpha _{2}&\alpha _{3}\\0&\alpha _{0}&\alpha _{1}&\alpha _{2}\\0&0&\alpha _{0}&\alpha _{1}\\0&0&0&\alpha _{0}\end{pmatrix}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75c757d2b31e8ec17d08b09cb1886d6e207bb735 height: height attribute not set width: width attribute not set description: {\displaystyle \pm i^{\frac {1}{2}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/commons-logo.svg/12px-commons-logo.svg.png height: 16 width: 12 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/wiktfavicon_en.svg/16px-wiktfavicon_en.svg.png height: 16 width: 16 description: no alt description found |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://de.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://de.wikipedia.org/static/images/footer/poweredby_mediawiki.svg height: 29 width: 84 description: powered by mediawiki |
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