Zeta and q-Zeta Functions and Associated Series and Integrals

Zeta and q-Zeta Functions and Associated Series and Integrals

1st Edition - October 11, 2011

Write a review

  • Authors: H. M. Srivastava, Junesang Choi
  • eBook ISBN: 9780123852199

Purchase options

Purchase options
DRM-free (PDF, EPub, Mobi)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order

Description

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals.

Key Features

  • Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Readership

Researchers, lecturers and postgraduate students in the fields of mathematical and applied sciences

Table of Contents

  • Preface

    Acknowledgements

    1. Introduction and Preliminaries

    1.1 Gamma and Beta Functions

    1.2 The Euler-Mascheroni Constant γ

    1.3 Polygamma Functions

    1.4 The Multiple Gamma Functions

    1.5 The Gaussian Hypergeometric Function and its Generalization

    1.6 Stirling Numbers of the First and Second Kind

    1.7 Bernoulli, Euler and Genocchi Polynomials and Numbers

    1.8 Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials and Numbers

    1.9 Inequalities for the Gamma Function and the Double Gamma Function

    Problems

    2. The Zeta and Related Functions

    2.1 Multiple Hurwitz Zeta Functions

    2.2 The Hurwitz (or Generalized) Zeta Function

    2.3 The Riemann Zeta Function

    2.4 Polylogarithm Functions

    2.5 Hurwitz–Lerch Zeta Functions

    2.6 Generalizations of the Hurwitz–Lerch Zeta Function

    2.7 Analytic Continuations of Multiple Zeta Functions

    Problems

    3. Series Involving Zeta Functions

    3.1 Historical Introduction

    3.2 Use of the Binomial Theorem

    3.3 Use of Generating Functions

    3.4 Use of Multiple Gamma Functions

    Problems

    4. Evaluations and Series Representations

    4.1 Evaluation of

    4.2 Rapidly Convergent Series for

    4.3 Further Series Representations

    4.4 Computational Results

    Problems

    5. Determinants of the Laplacians

    5.1 The n-Dimensional Problem

    5.2 Computations Using the Simple and Multiple Gamma Functions

    5.3 Computations Using Series of Zeta Functions

    5.4 Computations using Zeta Regularized Products

    5.5 Remarks and Observations

    Problems

    6. q-Extensions of Some Special Functions and Polynomials

    6.1 q-Shifted Factorials and q-Binomial Coefficients

    6.2 q-Derivative, q-Antiderivative and Jackson q-Integral

    6.3 q-Binomial Theorem

    6.4 q-Gamma Function and q-Beta Function

    6.5 A q-Extension of the Multiple Gamma Functions

    6.6 q-Bernoulli Numbers and q-Bernoulli Polynomials

    6.7 q-Euler Numbers and q-Euler Polynomials

    6.8 The q-Apostol-Bernoulli Polynomials of Order

    6.9 The q-Apostol-Euler Polynomials of Order

    6.10 A Generalized q-Zeta Function

    6.11 Multiple q-Zeta Functions

    Problems

    7. Miscellaneous Results

    7.1 A Set of Useful Mathematical Constants

    7.2 Log-Sine Integrals Involving Series Associated with the Zeta Function and Polylogarithms

    7.3 Applications of the Gamma and Polygamma Functions Involving Convolutions of the Rayleigh Functions

    7.4 Bernoulli and Euler Polynomials at Rational Arguments

    7.5 Closed-Form Summation of Trigonometric Series

    Problems

    Bibliography

Product details

  • No. of pages: 674
  • Language: English
  • Copyright: © Elsevier 2011
  • Published: October 11, 2011
  • Imprint: Elsevier
  • eBook ISBN: 9780123852199

About the Authors

H. M. Srivastava

Hari Mohan Srivastava works in the Department of Mathematics at University of Victoria, Victoria, British Columbia, BC, Canada

Affiliations and Expertise

Department of Mathematics, University of Victoria, Victoria, British Columbia, BC, Canada

Junesang Choi

Affiliations and Expertise

Dongguk University, Gyeongju, Republic of Korea

Ratings and Reviews

Write a review

There are currently no reviews for "Zeta and q-Zeta Functions and Associated Series and Integrals"