DLMF:18.28.E7 (Q5982)

No description defined

Language	Label	Description	Also known as
English	DLMF:18.28.E7	No description defined

Statements

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AlSalamChiharapolyQ{n}@{\cos@@{\theta}}{a}{b}{q}=\AskeyWilsonpolyp{n}@{\cos@@{\theta}}{a}{b}{0}{0}{q}=a^{-n}\sum_{\ell=0}^{n}q^{\ell}\frac{\qPochhammer{abq^{\ell}}{q}{n-\ell}\qPochhammer{q^{-n}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}\*\prod_{j=0}^{\ell-1}(1-2aq^{j}\cos@@{\theta}+a^{2}q^{2j})=\frac{\qPochhammer{ab}{q}{n}}{a^{n}}\qgenhyperphi{3}{2}@@{q^{-n},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,0}{q}{q}=\qPochhammer{be^{-\iunit\theta}}{q}{n}e^{\iunit n\theta}\qgenhyperphi{2}{1}@@{q^{-n},ae^{\iunit\theta}}{b^{-1}q^{1-n}e^{\iunit\theta}}{q}{b^{-1}qe^{-\iunit\theta}}.}

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DLMF id

DLMF:18.28.E7

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Symbols defined

Al-Salam–Chihara polynomial

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Symbols used

Askey–Wilson polynomial

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AskeyWilsonpolyp{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{d}}% {\NVar{q}}}

xml-id

C18.S28.E1.m2aadec

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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.m2abdec

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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.m2abdec

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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.m2abdec

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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.m2addec

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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.m2aadec

0 references

Q11728

test

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

xml-id

C18.S1.XMD3.m1ddec

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Q11744

test

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