Formula:KLS:01.14:04

<< Formula:KLS:01.14:03

formula in Some q-analogues of special functions

Formula:KLS:01.14:05 >>

${\displaystyle{\displaystyle{\displaystyle\lim\limits_{q\rightarrow 1}\mathrm{e}_{q}\!\left((1-q)z\right)=\lim\limits_{q\rightarrow 1}\mathrm{E}_{q}\!\left((1-q)z\right)={\mathrm{e}^{z}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the exponential function ${\displaystyle{\displaystyle{\displaystyle\mathrm{e}_{q}}}}$ used in KLS : http://drmf.wmflabs.org/wiki/Definition:qexpKLS
${\displaystyle{\displaystyle{\displaystyle\mathrm{E}_{q}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-analogue of the exponential function ${\displaystyle{\displaystyle{\displaystyle\mathrm{E}_{q}}}}$ used in KLS : http://drmf.wmflabs.org/wiki/Definition:qExpKLS
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

Bibliography

Equation in Section 1.14 of KLS.

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<< Formula:KLS:01.14:03

formula in Some q-analogues of special functions

Formula:KLS:01.14:05 >>