I have heard that there are ways to express sums of rational functions in terms of polygamma functions, and I would like to read more about it. However, I don't know the literature about special functions very well. Can anybody suggest possible references? Thank you.

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    $\begingroup$ this is explained on Wikipedia: en.wikipedia.org/wiki/… $\endgroup$ – Carlo Beenakker Dec 3 '19 at 10:39
  • $\begingroup$ @CarloBeenakker Yes, I have read that page indeed. I was wondering if there are some more "formal" sources, maybe also with some extra background information $\endgroup$ – Maurizio Moreschi Dec 3 '19 at 10:53

a journal publication with many generalisations is

Infinite sums as linear combinations of polygamma functions, Kh. Hessami Pilehrood, T. Hessami Pilehrood, Acta Arithmetica 130 (2007) 231-254.

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  • $\begingroup$ Thank you, this will do! Don't get me wrong, I am fond of wikipedia, I just wanted to go a bit more in deep into the subject. $\endgroup$ – Maurizio Moreschi Dec 3 '19 at 11:59

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