Vistas of Special Functions by Shigeru Kanemitsu (PDF)

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.

User’s Reviews

Editorial Reviews: Review This book is well structured, clearly written and almost entirely self-contained … It could be of interest to anyone interested in these topics; it is rather easily accessible to the beginner in the field as well as a valuable reference for those who know the subject matter well. Altogether this is an ideal book for those wishing to start research in this area. –Mathematical ReviewsThis book is well structured, clearly written and almost entirely self-contained … It could be of interest to anyone interested in these topics; it is rather easily accessible to the beginner in the field as well as a valuable reference for those who know the subject matter well. Altogether this is an ideal book for those wishing to start research in this area. –Mathematical Reviews From the Back Cover 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.

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