
Zeta and q-Zeta Functions and Associated Series and Integrals
Description
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
Affiliations and Expertise
Junesang Choi
Affiliations and Expertise
Ratings and Reviews
There are currently no reviews for "Zeta and q-Zeta Functions and Associated Series and Integrals"