Vistas of Special Functions .

Format:

Book

Author/Creator:

Chakraborty, Kalyan, Author.

Kanemitsu, Shigeru Tsukada, Haruo, Author, Author.

Language:

English

Subjects (All):

Functions, Special.

Bernoulli polynomials.

Physical Description:

1 online resource (228 p.)

Edition:

1st ed.

Place of Publication:

Singapore, SGP World Scientific Publishing Co. 20091001

Language Note:

English

Summary:

This book (Vistas 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.

Contents:

Intro

Contents

Preface

1. The theory of Bernoulli and allied polynomials

2. The theory of the gamma and related functions

2.1 Gamma function

2.2 The Euler digamma function

3. The theory of the Hurwitz-Lerch zeta-functions

3.1 Introduction

3.2 Integral representations

3.3 A formula of Ramanujan

3.4 Some definite integrals

3.5 The functional equation

4. The theory of Bernoulli polynomilas via zeta-functions

5. The theory of the gamma and related functions via zeta-functions

5.1 Derivatives of the Hurwitz zeta-function

5.2 Asymptotic formulas for the Hurwitz and related zetafunctions in the second variable

5.3 An application of the Euler digamma function

5.4 The first circle

6. The theory of Bessel functions and the Epstein zeta-functions

6.1 Introduction and the theory of Bessel functions

6.2 The theory of Epstein zeta-functions

6.3 Lattice zeta-functions

6.4 Bessel series expansions for Epstein zeta-functions

7. Fourier series and Fourier transforms

7.1 Fourier series

7.2 Integral transforms

7.3 Fourier transform

7.4 Mellin transform

8. Around Dirichlet's L-functions

8.1 The theory of periodic Dirichlet series

8.2 The Dirichlet class number formula

8.3 Proof of the theorems

Appendix A Complex functions

A.1 Function series

A.2 Residue theorem and its applications

Appendix B Summation formulas and convergence theorems

B.1 Summation formula and its applications

B.2 Application to the Riemann zeta-function

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

9786612758188

9781282758186

1282758187

9789814273985

9814273988

OCLC:

694144343