Overview

This is an introductory volume on the theory of basic Fourier series, a contemporary 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.

Full Product Details

Author:   Sergei Suslov
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2003 ed.
Volume:   9
Dimensions:   Width: 15.60cm , Height: 2.20cm , Length: 23.40cm
Weight:   1.600kg
ISBN:  

9781402012211

ISBN 10:   1402012217
Pages:   372
Publication Date:   31 March 2003
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Introduction.- 2. Basic Exponential and Trigonometric Functions.- 3. Addition Theorems.- 4. Some Expansions and Integrals.- 5. Introduction of Basic Fourier Series.- 6. Investigation of Basic Fourier Series.- 7. Completeness of Basic Trigonometric Systems.- 8. Improved Asymptotics of Zeros.- 9. Some Expansions in Basic Fourier Series.- 10. Basic Bernoulli and Euler Polynomials and Numbers and q-Zeta, Function.- 11. Numerical Investigation of Basic Fourier Series.- 12. Suggestions for Further Work.- Appendix A. Selected Summation and Transformation Formulas and.- Integrals.- A.l. Basic Hypergeometric Series.- A.2. Selected Summation Formulas.- A.3. Selected Transformation Formulas.- A.4. Some Basic Integrals.- Appendix B. Some Theorems of Complex Analysis.- B.l. Entire Functions.- B.2. Lagrange Inversion Formula.- B.3. Dirichlet Series.- B.4. Asymptotics.- Appendix C. Tables of Zeros of Basic Sine and Cosine Functions.- Appendix D. Numerical Examples of Improved Asymptotics.- Appendix E. Numerical Examples of Euler-Rayleigh Method.- Appendix F. Numerical Examples of Lower and Upper Bounds.

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