Vistas Of Special Functions
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Vistas Of Special Functions
Author: Shigeru Kanemitsu
language: en
Publisher: World Scientific
Release Date: 2007-06-07
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.
Vistas of Special Functions
1. The theory of Bernoulli and allied polynomials -- 2. The theory of the gamma and related functions -- 3. The theory of the Hurwitz-Lerch zeta-functions -- 4. The theory of Bernoulli polynomials via zeta functions -- 5. The theory of the gamma and related functions via zeta-functions -- 6. The theory of Bessel functions and the Epstein zeta-functions -- 7. Fourier series and Fourier transforms -- 8. Around Dirichlet's L-functions.
Vistas Of Special Functions Ii
This book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations — avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vista II will provide the reader ample opportunity to find suitable formulas and the means to apply them to practical problems for actual research. It can even be used during tutorials for paper writing.