Difference between revisions of "Polygamma"
From specialfunctionswiki
| Line 1: | Line 1: | ||
The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula | The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula | ||
$$\psi^{(m)}(z) = \dfrac{d^m}{dz^m} \log \Gamma(z),$$ | $$\psi^{(m)}(z) = \dfrac{d^m}{dz^m} \log \Gamma(z),$$ | ||
| − | where $\log$ denotes the [[logarithm]] and $\Gamma$ denotes the [[ | + | where $\log$ denotes the [[logarithm]] and $\log \Gamma$ denotes the [[loggamma]] function. The [[digamma]] function $\psi$ is the function $\psi^{(0)}(z)$ and the [[trigamma]] function is $\psi^{(1)}(z)$. |
=See Also= | =See Also= | ||
Revision as of 18:39, 3 June 2016
The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula $$\psi^{(m)}(z) = \dfrac{d^m}{dz^m} \log \Gamma(z),$$ where $\log$ denotes the logarithm and $\log \Gamma$ denotes the loggamma function. The digamma function $\psi$ is the function $\psi^{(0)}(z)$ and the trigamma function is $\psi^{(1)}(z)$.
