Summability Calculus

A Comprehensive Theory of Fractional Finite Sums

  • Ibrahim M.¬†Alabdulmohsin

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ibrahim M. Alabdulmohsin
    Pages 1-19
  3. Ibrahim M. Alabdulmohsin
    Pages 21-54
  4. Ibrahim M. Alabdulmohsin
    Pages 55-63
  5. Ibrahim M. Alabdulmohsin
    Pages 65-91
  6. Ibrahim M. Alabdulmohsin
    Pages 93-113
  7. Ibrahim M. Alabdulmohsin
    Pages 115-131
  8. Ibrahim M. Alabdulmohsin
    Pages 133-149
  9. Back Matter
    Pages 151-165

About this book

Introduction

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.   

Keywords

Fractional Finite Sums Analytic Summability Theory Divergent Series Special Functions Finite Differences Riemann Zeta Function Numerical Integration Series Acceleration Matrix Summability Methods Asymptotic Expansions Euler-Maclaurin Summation Formula Bernoulli Numbers Euler-Mascheroni constant Gamma and Polygamma functions

Authors and affiliations

  • Ibrahim M.¬†Alabdulmohsin
    • 1
  1. 1.King Abdullah University of Science and TechnologyDhahranSaudi Arabia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74648-7
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74647-0
  • Online ISBN 978-3-319-74648-7
  • About this book
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