Formula:KLS:01.08:05

<< Formula:KLS:01.08:04

formula in The q-shifted factorial

Formula:KLS:01.08:06 >>

${\displaystyle{\displaystyle{\displaystyle\lim\limits_{q\rightarrow 1}\frac{\left(q^{\alpha};q\right)_{k}}{(1-q)^{k}}={\left(\alpha\right)_{k}}}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 1.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:01.08:04

formula in The q-shifted factorial

Formula:KLS:01.08:06 >>