Summability Calculus

A Comprehensive Theory of Fractional Finite Sums
1. Auflage 2018
ISBN: 978-3-319-74647-0
Verlag: Springer International Publishing

Buch, Englisch, 165 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2818 g

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 developedfrom scratch using only undergraduate mathematics, such as calculus and linear algebra.

Zielgruppe

Research

Autoren/Hrsg.

Alabdulmohsin, Ibrahim M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

Ibrahim M. Alabdulmohsin is a postdoctoral fellow at the Department of Computer Science at the King Abdullah University of Science and Technology in Saudi Arabia.