Formula:KLS:14.05:60

<< Formula:KLS:14.05:58

formula in Big q-Jacobi

Formula:KLS:14.05:62 >>

${\displaystyle{\displaystyle{\displaystyle h_{0}=\int_{z_{-}q^{\mathbb{Z}}\cup z_{+}q^{\mathbb{Z}}}\frac{\left(ax,bx;q\right)_{\infty}}{\left(cx,dx;q\right)_{\infty}}d_{q}x}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle h_{0}=(1-q)c\frac{\left(q,-d/c,-qc/d,q^{2}ab;q\right)_{\infty}}{\left(qa,qb,-qbc/d,-qad/c;q\right)_{\infty}}}}}$ &
${\displaystyle{\displaystyle{\displaystyle h_{0}=(1-q)z_{+}\frac{\left(q,a/c,a/d,b/c,b/d;q\right)_{\infty}}{\left(ab/(qcd);q\right)_{\infty}}\frac{\theta(z_{-}/z_{+},cdz_{-}z_{+};q)}{\theta(cz_{-},dz_{-},cz_{+},dz_{+};q)}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.5 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.05:58

formula in Big q-Jacobi

Formula:KLS:14.05:62 >>