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An Introduction to Special Functions

  • Carlo Viola

Part of the UNITEXT book series (UNITEXT, volume 102)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 102)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Carlo Viola
    Pages 1-14
  3. Carlo Viola
    Pages 15-25
  4. Carlo Viola
    Pages 27-38
  5. Carlo Viola
    Pages 39-48
  6. Carlo Viola
    Pages 49-66
  7. Carlo Viola
    Pages 67-92
  8. Carlo Viola
    Pages 93-113
  9. Carlo Viola
    Pages 115-163
  10. Back Matter
    Pages 165-168

About this book

Introduction

The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in "higher calculus" and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.

Keywords

Analytic functions opf one complex variable Picard theorems Weierstrass factorization Bernoulli numbers Bernoulli polynomials Summation formulae Euler gamma-function Hypergeometric functions

Authors and affiliations

  • Carlo Viola
    • 1
  1. 1.Department of MathematicsUniversity of PisaPisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-41345-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-41344-0
  • Online ISBN 978-3-319-41345-7
  • Series Print ISSN 2038-5714
  • Buy this book on publisher's site