Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals
✍ Scribed by Junesang Choi; H. M. Srivastava
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 162 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
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)