Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions,multiple Euler sums and log‐sine integrals |
| |
| Authors: | Junesang Choi H. M. Srivastava |
| |
| Affiliation: | 1. Department of Mathematics, Dongguk University, Kyongju (Gyeongju) 780‐714, Republic of Korea;2. Phone: +82 054 770 2262, Fax: +82 054 770 2526;3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada |
| |
| 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) |
| |
| Keywords: | Gamma function psi‐function polygamma functions Euler sums Goldbach− Euler series convolutions of Rayleigh functions Gauss summation theorem series associated with the Zeta function Riemann Zeta function Hurwitz Zeta function log‐sine integrals |
|
|
