# Formula:KLS:14.05:38

$\displaystyle {\displaystyle \frac{h_n}{h_0}=q^{\frac12 n(n-1)}\left(\frac{q^2a^2d}c\right)^n \frac{1-qab}{1-q^{2n+1}ab} \frac{\qPochhammer{q,qb,-qbc/d}{q}{n}}{\qPochhammer{qa,qab,-qad/c}{q}{n}} =(-1)^n\left(\frac{c^2}{ab}\right)^n q^{\frac12 n(n-1)} q^{2n} \frac{\qPochhammer{q,qd/a,qd/b}{q}{n}}{\qPochhammer{qcd/(ab),qc/a,qc/b}{q}{n}} \frac{1-qcd/(ab)}{1-q^{2n+1}cd/(ab)} }$

## Substitution(s)

$\displaystyle {\displaystyle h_0=(1-q)c \frac{\qPochhammer{q,-d/c,-qc/d,q^2ab}{q}{\infty}} {\qPochhammer{qa,qb,-qbc/d,-qad/c}{q}{\infty}}}$ &
$\displaystyle {\displaystyle h_0 =(1-q)z_+ \frac{\qPochhammer{q,a/c,a/d,b/c,b/d}{q}{\infty}}{\qPochhammer{ab/(qcd)}{q}{\infty}} \frac{\theta(z_-/z_+,cdz_-z_+;q)}{\theta(cz_-,dz_-,cz_+,dz_+;q)}}$

## 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