Difference between revisions of "Polygamma recurrence relation"

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==References==
 
==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Value of polygamma at positive integer plus 1/2|next=Polygamma reflection formula}}: 6.4.6
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Value of derivative of trigamma at positive integer plus 1/2|next=Polygamma reflection formula}}: 6.4.6
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Revision as of 20:23, 11 June 2016

Theorem

The following formula holds: $$\psi^{(m)}(z+1)=\psi^{(m)}(z)+\dfrac{(-1)^mm!}{z^{m+1}},$$ where $\psi^{(m)}$ denotes the polygamma and $m!$ denotes the factorial.

Proof

References