Formula:KLS:01.15:15

<< Formula:KLS:01.15:14

formula in The q-derivative and q-integral

Formula:KLS:01.15:16 >>

${\displaystyle{\displaystyle{\displaystyle\int_{a}^{b}g(x)\qderiv{q}f(x)\,d_{q}x=\Big{[}f(x)g(x)\Big{]}_{a}^{b}-\int_{a}^{b}f(qx)\qderiv{q}g(x)\,d_{q}x}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv

Bibliography

Equation in Section 1.15 of KLS.

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<< Formula:KLS:01.15:14

formula in The q-derivative and q-integral

Formula:KLS:01.15:16 >>