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Introduction to Basic Fourier Series

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ISBN-10: 1402012217

ISBN-13: 9781402012211

Edition: 2003

Authors: Sergei K. Suslov

List price: $249.99
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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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Book details

List price: $249.99
Copyright year: 2003
Publisher: Springer
Publication date: 3/31/2003
Binding: Hardcover
Pages: 372
Size: 9.50" wide x 9.50" long x 1.00" tall
Weight: 1.628
Language: English

Foreword
Preface
Introduction
Basic Exponential and Trigonometric Functions
Addition Theorems
Some Expansions and Integrals
Introduction of Basic Fourier Series
Investigation of Basic Fourier Series
Completeness of Basic Trigonometric Systems
Improved Asymptotics of Zeros
Some Expansions in Basic Fourier Series
Basic Bernoulli and Euler Polynomials and Numbers and q-Zeta Function
Numerical Investigation of Basic Fourier Series
Suggestions for Further Work
Selected Summation and Transformation Formulas and Integrals
Basic Hypergeometric Series
Selected Summation Formulas
Selected Transformation Formulas
Some Basic Integrals
Some Theorems of Complex Analysis
Entire Functions
Lagrange Inversion Formula
Dirichlet Series
Asymptotics
Tables of Zeros of Basic Sine and Cosine Functions
Numerical Examples of Improved Asymptotics
Numerical Examples of Euler-Rayleigh Method
Numerical Examples of Lower and Upper Bounds
Bibliography
Index