Difference between revisions of "Q-Polygamma function"
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(Created page with "The $q$-polygamma functions of order $m$, $\psi_q^{(m)}$, are analogues of the polygamma function defined by $$\psi_q^{(m)}(z)=\dfrac{\partial^m}{\partial z^m} \psi_q(z),$...") |
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$$\psi_q^{(m)}(z)=\dfrac{\partial^m}{\partial z^m} \psi_q(z),$$ | $$\psi_q^{(m)}(z)=\dfrac{\partial^m}{\partial z^m} \psi_q(z),$$ | ||
where $\psi_q(z) = \dfrac{1}{\Gamma_q(z)} \dfrac{\partial}{\partial z} \Gamma_q(z).$ Here the function $\Gamma_q$ is the [[q-Gamma function|$q$-Gamma function]]. | where $\psi_q(z) = \dfrac{1}{\Gamma_q(z)} \dfrac{\partial}{\partial z} \Gamma_q(z).$ Here the function $\Gamma_q$ is the [[q-Gamma function|$q$-Gamma function]]. | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 18:56, 24 May 2016
The $q$-polygamma functions of order $m$, $\psi_q^{(m)}$, are analogues of the polygamma function defined by $$\psi_q^{(m)}(z)=\dfrac{\partial^m}{\partial z^m} \psi_q(z),$$ where $\psi_q(z) = \dfrac{1}{\Gamma_q(z)} \dfrac{\partial}{\partial z} \Gamma_q(z).$ Here the function $\Gamma_q$ is the $q$-Gamma function.
