Formula:6668

Digital Library of Mathematical Functions ID 18.27.E21

${\displaystyle{\displaystyle h_{n}\left(x;q\right)=\left(q;q\right)_{n}\sum_{\ell=0}^{\left\lfloor n/2\right\rfloor}\frac{(-1)^{\ell}q^{\ell(\ell-1)}x^{n-2\ell}}{\left(q^{2};q^{2}\right)_{\ell}\left(q;q\right)_{n-2\ell}}=x^{n}{{}_{2}\phi_{0}}\left({q^{-n},q^{-n+1}\atop-};q^{2},x^{-2}q^{2n-1}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$:
• ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$:
• ${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$: basic hypergeometric (or $$q$$ -hypergeometric) function
• ${\displaystyle{\displaystyle q}}$: real variable
• ${\displaystyle{\displaystyle\ell}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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