Difference between revisions of "Q-Gamma at z+1"

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(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...")
 
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==Theorem==
<strong>[[Q-Gamma at z+1|Theorem]]:</strong> The following formula holds:
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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 $z$.
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Revision as of 21:17, 4 July 2016

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 $z$.

Proof

References