Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log‐sine integrals | Zendy

Choi Junesang | Zendy; Srivastava H. M. | Zendy

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Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log‐sine integrals

Author(s) -

Choi Junesang,

Srivastava H. M.

Publication year - 2009

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200710032

Subject(s) - mathematics , parameterized complexity , logarithm , euler's formula , gamma function , sine , series (stratigraphy) , class (philosophy) , function (biology) , pure mathematics , identity (music) , mathematical analysis , combinatorics , paleontology , geometry , artificial intelligence , evolutionary biology , computer science , biology , physics , acoustics

The Gamma function and its n th logarithmic derivatives (that is, the polygamma or the psi‐functions) have found many interesting and useful applications in a variety of subjects in pure and applied mathematics. Here we mainly apply these functions to treat convolutions of the Rayleigh functions by recalling a general identity expressing a certain class of series as psi‐functions and to evaluate a class of log‐sine integrals in an algorithmic way. We also evaluate some Euler sums and give much simpler psi‐function expressions for some known parameterized multiple sums (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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