Summability Calculus A Comprehensive Theory of Fractional Finite Sums /

• Main Author: Alabdulmohsin, Ibrahim M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Number theory.; Functions of real variables.; Special functions.; Differential equations.; Sequences (Mathematics).; Approximation theory.; Number Theory.; Real Functions.; Special Functions.; Ordinary Differential Equations.; Sequences, Series, Summability.; Approximations and Expansions.

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. Imp...

Table of Contents:

• 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.