Formula:KLS:01.15:01

<< Some q-analogues of special functions

formula in The q-derivative and q-integral

Formula:KLS:01.15:02 >>

${\displaystyle{\displaystyle{\displaystyle{}\mathcal{D}_{q}f(z):=\left\{\begin{array}[]{ll}\displaystyle\frac{f(z)-f(qz)}{(1-q)z},&z\neq 0\\ f^{\prime}(0),&z=0.\end{array}\right.}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv

Bibliography

Equation in Section 1.15 of KLS.

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<< Some q-analogues of special functions

formula in The q-derivative and q-integral

Formula:KLS:01.15:02 >>