Overview
The first book in the literature, which is devoted to fractional finite sums as an object of study on its own right
Unifies many disparate historical results in the works of prominent mathematicians, such as Gregory, Euler, Boole, and Ramanujan, and shows how such results relate to each other in significant ways
Contains new materials and identities that have not been published before
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Table of contents (7 chapters)
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
- ordinary differential equations
About this book
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.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Summability Calculus
Book Subtitle: A Comprehensive Theory of Fractional Finite Sums
Authors: Ibrahim M. Alabdulmohsin
DOI: https://doi.org/10.1007/978-3-319-74648-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-74647-0Published: 15 March 2018
eBook ISBN: 978-3-319-74648-7Published: 07 March 2018
Edition Number: 1
Number of Pages: XIII, 165
Topics: Number Theory, Real Functions, Special Functions, Ordinary Differential Equations, Sequences, Series, Summability, Approximations and Expansions