Formula:KLS:01.15:17

<< Formula:KLS:01.15:16

formula in The q-derivative and q-integral

The q-derivative and q-integral >>

${\displaystyle{\displaystyle{\displaystyle\int_{a}^{b}\frac{\left(a^{-1}qt,b^{-1}qt;q\right)_{\infty}}{\left(dt,et;q\right)_{\infty}}\,d_{q}t=(b-a)(1-q)\,\frac{\left(q,a^{-1}bq,ab^{-1}q,abde;q\right)_{\infty}}{\left(ad,ae,bd,be;q\right)_{\infty}}}}}$

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

Bibliography

Equation in Section 1.15 of KLS.

URL links

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<< Formula:KLS:01.15:16

formula in The q-derivative and q-integral

The q-derivative and q-integral >>