Difference between revisions of "Polygamma"

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=References=
 
=References=
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Integral representaiton of polygamma for Re(z) greater than 0}}: 6.4.1
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Integral representation of polygamma for Re(z) greater than 0}}: 6.4.1
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 08:05, 11 June 2016

The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula $$\psi^{(m)}(z) = \dfrac{\mathrm{d}^{m+1}}{\mathrm{d}z^{m+1}} \log \Gamma(z),$$ where $\log \Gamma$ denotes the loggamma function. The digamma function $\psi$ is the function $\psi^{(0)}(z)$ and the trigamma function is $\psi^{(1)}(z)$.

Properties

Integral representation of polygamma
Integral representation of polygamma 2
Polygamma recurrence relation
Polygamma reflection relation
Polygamma series representation
Relation between polygamma and Hurwitz zeta

See Also

Digamma
Trigamma

References