DLMF:18.33.E15 (Q6025): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:18.33.E15	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{\left(aq^{2};q^% {2}\right)_{\ell}\left(a;q^{2}\right)_{n-\ell}}{\left(q^{2};q^{2}\right)_{\ell% }\left(q^{2};q^{2}\right)_{n-\ell}}(q^{-1}z)^{\ell}=\frac{\left(a;q^{2}\right)% _{n}}{\left(q^{2};q^{2}\right)_{n}}{{}_{2}\phi_{1}}\left({aq^{2},q^{-2n}\atop a% ^{-1}q^{2-2n}};q^{2},\frac{qz}{a}\right),}}

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DLMF:18.33.E15

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Defining formula

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

C17.S2.SS1.p1.m2adec

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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.m2adec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1mdec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1cdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1ldec

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Defining formula

{\displaystyle{\displaystyle\phi_{n}(z)}}

C18.S33.XMD1.m1ldec

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