Vistas of special functions
By: Shigeru Kanemitsu & Haruo Tsukada
Contributors: Tsukada, Haruo, 1961-
Publisher: World Scientific
Published: 2007
Place of publication: Singapore; Hackensack, NJ
Language: eng
Number of pages: 215
ISBN-13: 9789812707741
Subjects: Bernoulli polynomials; Special Functions
Description: This is a unique book for studying special functions through zeta-functions. Many important formulas of special functions scattered throughout the literature are located in their proper positions and readers get enlightened access to them in this book. The areas covered include: Bernoulli polynomials, the gamma function (the beta and the digamma function), the zeta-functions (the Hurwitz, the Lerch, and the Epstein zeta-function), Bessel functions, an introduction to Fourier analysis, finite Fourier series, Dirichlet L-functions, the rudiments of complex functions and summation formulas. The Fourier series for the (first) periodic Bernoulli polynomial is effectively used, familiarizing the reader with the relationship between special functions and zeta-functions.
Notes: Includes bibliographical references (p. 207-211) and index.
Table of contents: title: The theory of Bernoilli and allied polynomials; title: The theory of the gamma and related functions; title: The theory of the Hurwitz-Lerch zeta-functions; title: The theory of Bernoulli polynomilas [sic] via zeta-functions; title: The theory of the gamma and related functions via zeta-functions; title: The theory of Bessel functions and the Epstein zeta-functions; title: Fourier series and Fourier transforms; title: Around Dirichlet's L-functions; title: Appendix A : Complex functions; title: Appendix B : Summation formulas and convergence theorems.