Difference between revisions of "Q-Gamma at z+1"
From specialfunctionswiki
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$\Gamma_q(z+1)=\dfrac{1-q^z...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\Gamma_q(z+1)=\dfrac{1-q^z}{1-q}\Gamma_q(z),$$ | $$\Gamma_q(z+1)=\dfrac{1-q^z}{1-q}\Gamma_q(z),$$ | ||
where $\Gamma_q$ denotes the [[q-Gamma|$q$-gamma]] function and $[z]_q$ denotes the [[q-number|$q$-number]] of $z$. | where $\Gamma_q$ denotes the [[q-Gamma|$q$-gamma]] function and $[z]_q$ denotes the [[q-number|$q$-number]] of $z$. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | * {{PaperReference|The q-gamma function for q greater than 1|1980|Daniel S. Moak|prev=Q-shifted factorial|next=findme}} | ||
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:17, 30 May 2017
Theorem
The following formula holds: $$\Gamma_q(z+1)=\dfrac{1-q^z}{1-q}\Gamma_q(z),$$ where $\Gamma_q$ denotes the $q$-gamma function and $[z]_q$ denotes the $q$-number of $z$.
