Difference between revisions of "Polygamma"

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$$\psi^{(m)}(z) = \dfrac{d^m}{dz^m} \log \Gamma(z),$$
 
$$\psi^{(m)}(z) = \dfrac{d^m}{dz^m} \log \Gamma(z),$$
 
where $\log$ denotes the [[logarithm]] and $\log \Gamma$ denotes the [[loggamma]] function. The [[digamma]] function $\psi$ is the function $\psi^{(0)}(z)$ and the [[trigamma]] function is $\psi^{(1)}(z)$.
 
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 $\psi^{(1)}(z)$.
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<div align="center">
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<gallery>
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File:Complexdigammaplot.png|Domain coloring of $\psi^{(0)}(z)$.
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</gallery>
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</div>
  
 
=See Also=
 
=See Also=

Revision as of 18:49, 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 $\psi^{(1)}(z)$.

See Also

Digamma
Trigamma