# Formula:KLS:14.21:31

$\displaystyle {\displaystyle \frac{h_n}{h_0}=\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n} q^n},\qquad h_0 }$

## Substitution(s)

$\displaystyle {\displaystyle \frac{h_n}{h_0} =- \frac{\qPochhammer{q^{-\alpha}}{q}{\infty}}{\qPochhammer{q}{q}{\infty}} \frac\cpi{\sin@{\cpi\alpha}}}$ &
$\displaystyle {\displaystyle h_n=q^{-\frac12\alpha(\alpha+1)} \qPochhammer{q}{q}{\alpha} \log(q^{-1})\qquad(\alpha\in\ZZ_{\ge0})}$

## Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

## Symbols List

& : logical and
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
$\displaystyle {\displaystyle \mathrm{sin}}$  : sine function : http://dlmf.nist.gov/4.14#E1
$\displaystyle {\displaystyle \pi}$  : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
$\displaystyle {\displaystyle \mathrm{log}}$  : principle branch of logarithm logarithm : http://dlmf.nist.gov/4.2#E2