Balanced polygamma function: Difference between revisions

Revision as of 19:31, 25 May 2021

Revision as of 17:35, 27 May 2021

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or alternatively,

: <math>\psi(z,q)&nbsp;<s>^{<pre><blockquote><ref name="{{#tag:ref|<ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref><ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref></ref>|group="nb"|name=""}}" /></blockquote></pre>}</s>=e^{- \gamma z}\frac{\partial}{\partial z}\left(e^{\gamma z}\frac{\zeta(z+1,q)}{\Gamma(-z)}\right),</math>

where {{math|''ψ''(''z'')}} is the [[Polygamma function]] and {{math|''ζ''(''z'',''q'')}}, is the [[Hurwitz zeta function]].