An Introduction to Basic Fourier Series
By: by Sergei K. Suslov
Series: Developments in Mathematics -- 9; Developments in mathematics -- 9.
Publisher: Springer US
Published: 2003
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 371
ISBN-13: 9781441952448; 9781475737318
Subjects: Mathematics; Fourier analysis; Special Functions
Description: This is an introductory volume on a novel theory of basic Fourier series, a new interesting research area in classical analysis and q-series. This research utilizes approximation theory, orthogonal polynomials, analytic functions, and numerical methods to study the branch of q-special functions dealing with basic analogs of Fourier series and its applications. This theory has interesting applications and connections to general orthogonal basic hypergeometric functions, a q-analog of zeta function, and, possibly, quantum groups and mathematical physics. Audience: Researchers and graduate students interested in recent developments in q-special functions and their applications.
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Table of contents: title: Foreword; title: Preface; title: 1: Introduction; title: 2: Basic Exponential and Trigonometric Functions; title: 3: Addition Theorems; title: 4: Some Expansions and Integrals; title: 5: Introduction of Basic Fourier Series; title: 6: Investigation of Basic Fourier Series; title: 7: Completeness of Basic Trigonometric Systems; title: 8: Improved Asymptotics of Zeros; title: 9: Some Expansions in Basic Fourier Series; title: 10: Basic Bernoulli and Euler Polynomials and Numbers and q-Zeta Function; title: 11: Numerical Investigation of Basic Fourier Series; title: 12: Suggestions for Further Work; title: Appendix A: Selected Summation and Transformation Formulas and Integrals; title: A.1. Basic Hypergeometric Series; title: A.2. Selected Summation Formulas; title: A.3. Selected Transformation Formulas; title: A.4. Some Basic Integrals; title: Appendix B: Some Theorems of Complex Analysis; title: B.1. Entire Functions; title: B.2. Lagrange Inversion Formula; title: B.3. Dirichlet Series; title: B.4. Asymptotics; title: Appendix C: Tables of Zeros of Basic Sine and Cosine Functions; title: Appendix D: Numerical Examples of Improved Asymptotics; title: Appendix E: Numerical Examples of Euler-Rayleigh Method; title: Appendix F: Numerical Examples of Lower and Upper Bounds; title: Bibliography; title: Index.