Summability calculus : a comprehensive theory of fractional finite sums / Ibrahim M. Alabdulmohsin.
Alabdulmohsin, Ibrahim M., author.
2018
QA303.2
Available Online

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Title Summability calculus : a comprehensive theory of fractional finite sums / Ibrahim M. Alabdulmohsin.
Author Alabdulmohsin, Ibrahim M., author.
ISBN 9783319746487 (electronic book)
3319746480 (electronic book)
9783319746470
3319746472
DOI https://doi.org/10.1007/978-3-319-74648-7
Published Cham, Switzerland : Springer, 2018.
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-74648-7 doi
Call Number QA303.2
Dewey Decimal Classification 515
Summary 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.   .
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (viewed March 14, 2018).
Available in Other Form Print version: 9783319746470
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1 Introduction
2 Simple Finite Sums
3 Composite Finite Sums
4 Analytic Summability Theory
5 Oscillating Finite Sums
6 Computing Finite Sums
7 The Language of Finite Differences
The Sum of the Approximation Errors of Harmonic Numbers
Glossary
Index.

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