DLMF:18.28.E1 (Q5976)

No description defined

Language	Label	Description	Also known as
English	DLMF:18.28.E1	No description defined

Statements

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n}(\cos@@{\theta})=\AskeyWilsonpolyp{n}@{\cos@@{\theta}}{a}{b}{c}{d}{q}=a^{-n}\sum_{\ell=0}^{n}q^{\ell}\qmultiPochhammersym{abq^{\ell},acq^{\ell},adq^{\ell}}{q}{n-\ell}\*\frac{\qmultiPochhammersym{q^{-n},abcdq^{n-1}}{q}{\ell}}{\qPochhammer{q}{q}{\ell}}\prod_{j=0}^{\ell-1}{(1-2aq^{j}\cos@@{\theta}+a^{2}q^{2j})}=a^{-n}\qmultiPochhammersym{ab,ac,ad}{q}{n}\*\qgenhyperphi{4}{3}@@{q^{-n},abcdq^{n-1},ae^{\iunit\theta},ae^{-\iunit\theta}}{ab,ac,ad}{q}{q}.}

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DLMF id

DLMF:18.28.E1

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Symbols defined

Askey–Wilson 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.m2adec

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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.m2adec

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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.m2adec

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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.m2adec

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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.m2adec

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Q11713

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}}

xml-id

C17.S2.SS1.p1.m6adec

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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.m1dec

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Q11744

test

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

xml-id

C18.S1.XMD4.m1dec

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Q11726

test

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

xml-id

C18.S1.XMD6.m1dec

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Q11731

test

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

xml-id

C18.S1.XMD9.m1dec

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Q11727

test

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

xml-id

C18.S2.XMD3.m1dec

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