The most complete reference for identities and special values for polylogarithm and polygamma functions

Question

I am looking for a book, paper, web site, etc. (or several ones) containing the most complete list of identities and special values for the polylogarithm $\operatorname{Li}_s(z)$ and polygamma $\psi^{(a)}(z)$ functions, including generalizations to negative, non-integer and complex orders and arguments.

As far as I know, there is an ongoing research in this area, and many new and curious identities occur from time to time. Here is the list of resources I found so far:

Dilogarithm at Wikipedia
Dilogarithm at MathWorld
PolyLog at The Wolfram Functions Site
Trilogarithm at MathWorld
Polylogarithm at Wikipedia
Digamma Function at Wikipedia
Digamma Function at MathWorld
Trigamma Function at MathWorld
PolyGamma at The Wolfram Functions Site

Anatol Kirillov, Dilogarithm identities, available from http://arxiv.org/abs/hep--th/9408113 — gammatester, Nov 08 '13 at 08:35
Dear Vladimir, I see you are also interested in the polylogarithm function. Are you willing to discuss some topics related to it? For instance I have the following question on its connection with Bernoulli polynomials.: Connection between the polylogarithm and the Bernoulli polynomials. — Dr Potato, Feb 14 '24 at 14:39

score 17 · Answer 1 · answered Nov 16 '13 at 13:46

17

My preferred books on the topics

Lewin L. Polylogarithms and associated functions (NH, 1981)

Lewin L. (ed.) Structural properties of polylogarithms (AMS, 1991)

H. M. Srivastava, Choi Junesang, Zeta and q-Zeta Functions and Associated Series and Integrals. (Elsevier,2011)

answered Nov 16 '13 at 13:46

alexjo

15,328

Thanks! Both answers are useful, so I decided to accept the first one, but award the bounty to yours. Hopefully, it does not feel unfair to anyone. – Vladimir Reshetnikov Nov 16 '13 at 17:23
12

Lewin book price: $\large$\ \color{#c00000}{599.95}$ !!! – Felix Marin Aug 21 '14 at 08:20
2

@FelixMarin at least it's not $600! – clathratus Dec 12 '20 at 21:45

score 15 · Accepted Answer · answered Nov 07 '13 at 19:33

15

DLMF cites Lewin (1981), Kölbig (1986), Maximon (2003), Prudnikov et al. which can be found in the bibliography of Dlmf.

answered Nov 07 '13 at 19:33

Sophia Antipolis

400

The most complete reference for identities and special values for polylogarithm and polygamma functions

2 Answers2

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