Umfang:
Online Ressource (1 v.)
Ausgabe:
Rev. ed.
Ausgabe:
Online-Ausg.
ISBN:
0123852188
,
9780123852182
,
9780123852199
,
1283298996
,
9781283298995
Inhalt:
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 as 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. 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
Inhalt:
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 as 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. 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
Anmerkung:
Includes bibliographical references. - Description based on print version record
,
Chapter 1. Introduction and Preliminaries -- Chapter 2. The Zeta and Related Functions -- Chapter 3. Series Involving Zeta Functions -- Chapter 4. Evaluations and Series Representations -- Chapter 5. Determinants of the Laplacians -- Chapter 6. q-Extensions of some special functions and polynomials -- Chapter 7. Miscellaneous Results -- Bibliography.
,
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 as 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. 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
,
Front cover; Zeta and q-Zeta Functionsand Associated Series andIntegrals; Copyright; Table of contents; Preface; Acknowledgements; Chapter 1. Introduction and Preliminaries; 1.1 Gamma and Beta Functions; The Gamma Function; Pochhammer's Symbol and the Factorial Function; Multiplication Formulas of Legendre and Gauss; Stirling's Formula for n! and its Generalizations; The Beta Function; The Incomplete Gamma Functions; The Incomplete Beta Functions; The Error Functions; The Bohr-Mollerup Theorem; 1.2 The Euler-Mascheroni Constant γ; A Set of Known Integral Representations for γ
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Further Integral Representations for γFrom an Application of the Residue Calculus; 1.3 Polygamma Functions; The Psi (or Digamma) Function; Integral Representations for ψ(z); Gauss's Formulas for ψ(p/q); Special Values of ψ(z); The Polygamma Functions; Special Values of ψ(n)(z); The Asymptotic Expansion for ψ(z); 1.4 The Multiple Gamma Functions; The Double Gamma Function Γ2; Integral Formulas Involving the Double Gamma Function; The Evaluation of an Integral Involving log G(z); The Multiple Gamma Functions; The Triple Gamma Function Γ3; A Multiplication Formula for the Γn
,
1.5 The Gaussian Hypergeometric Function and its GeneralizationThe Gauss Hypergeometric Equation; Gauss's Hypergeometric Series; The Hypergeometric Series and Its Analytic Continuation; Linear, Quadratic and Cubic Transformations; Hypergeometric Representations of Elementary Functions; Hypergeometric Representations of Other Functions; The Confluent Hypergeometric Function; Important Properties of Kummer's Confluent Hypergeometric Function; The Generalized (Gauss and Kummer) Hypergeometric Function; Analytic Continuation of the Generalized Hypergeometric Function
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Functions Expressible in Terms of the pFq Function1.6 Stirling Numbers of the First and Second Kind; Stirling Numbers of the First Kind; Stirling Numbers of the Second Kind; Relationships Among Stirling Numbers of the First and Second Kind and Bernoulli Numbers; 1.7 Bernoulli, Euler and Genocchi Polynomials and Numbers; Bernoulli Polynomials and Numbers; The Generalized Bernoulli Polynomials and Numbers; Euler Polynomials and Numbers; Fourier Series Expansions of Bernoulli and Euler Polynomials; Relations Between Bernoulli and Euler Polynomials; The Generalized Euler Polynomials and Numbers
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Genocchi Polynomials and Numbers1.8 Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials and Numbers; Apostol-Bernoulli Polynomials and Numbers; Apostol-Genocchi Polynomials and Numbers; Important Remarks and Observations; Generalizations and Unified Presentations of the Apostol Type Polynomials; 1.9 Inequalities for the Gamma Function and the Double Gamma Function; The Gamma Function and Its Relatives; The Double Gamma Function; Problems; Chapter 2. The Zeta and Related Functions; 2.1 Multiple Hurwitz Zeta Functions; The Analytic Continuation of ζn (s,a)
,
Relationship between ζn (s,x) and B n (α)(x)
Weitere Ausg.:
ISBN 9780123852182
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Zeta and q-Zeta functions and associated series and integrals
Sprache:
Englisch
Schlagwort(e):
Electronic books
;
Electronic books
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