特殊関数の展望 Vistas of Special Functions

Kanemitsu, Shigeru/ Tsukada, Haruo

World Scientific Publishing Co Pte Ltd（2007/06発売）

• 製本 Hardcover:ハードカバー版／ページ数 228 p.
• 言語 ENG
• 商品コード 9789812707741
• DDC分類 515.5

基本説明

A unique book for studying special functions through zeta-functions.

Full 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.

Contents

Bernoulli Polynomials; The Gamma Function; The Hurwitz Zeta-Function; Bernoulli Polynomials via the Hurwitz Zeta-Function; The Gamma Function via the Hurwitz Zeta-Function; Bessel Functions and Crystal Symmetry; Fourier Series and Fourier Transforms; Finite Fourier Series.