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Summability Calculus : A Comprehensive Theory of Fractional Finite Sums / / by Ibrahim M. Alabdulmohsin



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Autore: Alabdulmohsin Ibrahim M Visualizza persona
Titolo: Summability Calculus : A Comprehensive Theory of Fractional Finite Sums / / by Ibrahim M. Alabdulmohsin Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
Edizione: 1st ed. 2018.
Descrizione fisica: 1 online resource (XIII, 165 p.)
Disciplina: 515
Soggetto topico: 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
Nota di contenuto: 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.
Sommario/riassunto: 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.   .
Titolo autorizzato: Summability Calculus  Visualizza cluster
ISBN: 3-319-74648-0
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910300124403321
Lo trovi qui: Univ. Federico II
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