DLMF:18.28.E13 (Q5988)

No description defined

Language	Label	Description	Also known as
English	DLMF:18.28.E13	No description defined

Statements

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \contqultrasphpoly{n}@{\cos@@{\theta}}{\beta}{q}=\sum_{\ell=0}^{n}\frac{\qPochhammer{\beta}{q}{\ell}\qPochhammer{\beta}{q}{n-\ell}}{\qPochhammer{q}{q}{\ell}\qPochhammer{q}{q}{n-\ell}}e^{\iunit(n-2\ell)\theta}=\frac{\qPochhammer{\beta}{q}{n}}{\qPochhammer{q}{q}{n}}e^{\iunit n\theta}\qgenhyperphi{2}{1}@@{q^{-n},\beta}{\beta^{-1}q^{1-n}}{q}{\beta^{-1}qe^{-2\iunit\theta}}.}

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DLMF id

DLMF:18.28.E13

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Symbols defined

continuous $$q$$ -ultraspherical polynomial

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Symbols used

cosine function

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}

xml-id

C4.S14.E2.m2addec

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base of natural logarithm

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

xml-id

C4.S2.E11.m2addec

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imaginary unit

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}

xml-id

C1.S9.E1.m2aedec

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Q11298

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}

xml-id

C17.S2.SS1.p1.m2ahdec

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basic hypergeometric (or $$q$$ -hypergeometric) function

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}}

xml-id

C17.S4.E1.m2acdec

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Q11728

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}

xml-id

C18.S1.XMD3.m1jdec

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Q11744

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}