DLMF:18.28.E16 (Q5991)

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Language	Label	Description	Also known as
English	DLMF:18.28.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle H_{n}\left(\cos\theta\,|\,q\right)=\sum_{\ell=0}^% {n}\frac{\left(q;q\right)_{n}e^{\mathrm{i}(n-2\ell)\theta}}{\left(q;q\right)_{% \ell}\left(q;q\right)_{n-\ell}}=e^{\mathrm{i}n\theta}{{}_{2}\phi_{0}}\left({q^% {-n},0\atop-};q,q^{n}e^{-2\mathrm{i}\theta}\right).}}

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DLMF:18.28.E16

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Symbols defined

continuous $$q$$ -Hermite polynomial

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2agdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2agdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

C17.S2.SS1.p1.m2akdec

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

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E1.m2aedec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1mdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1kdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1fdec

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Sitelinks

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