Formula:KLS:01.15:19

<< Formula:KLS:01.15:18

formula in The q-derivative and q-integral

Formula:KLS:01.16:01 >>

${\displaystyle{\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{1}{\left(dt,et;q\right)_{\infty}}\,d_{q}t{}=(1-q)\,\frac{\left(q,-q,-1,-de,-d^{-1}{\mathrm{e}^{-1}}q;q\right)_{\infty}}{\left(d,-d,d^{-1}q,-d^{-1}q,e,-e,{\mathrm{e}^{-1}}q,-{\mathrm{e}^{-1}}q;q\right)_{\infty}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\int}}}$ : 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
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

Bibliography

Equation in Section 1.15 of KLS.

URL links

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<< Formula:KLS:01.15:18

formula in The q-derivative and q-integral

Formula:KLS:01.16:01 >>