03875nam 22006495 450 991030012440332120200704152547.03-319-74648-010.1007/978-3-319-74648-7(CKB)4100000002892343(MiAaPQ)EBC5357979(DE-He213)978-3-319-74648-7(PPN)225553619(EXLCZ)99410000000289234320180307d2018 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSummability Calculus A Comprehensive Theory of Fractional Finite Sums /by Ibrahim M. Alabdulmohsin1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XIII, 165 p.) 3-319-74647-2 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.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.   .Number theoryFunctions of real variablesSpecial functionsDifferential equationsSequences (Mathematics)Approximation theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Real Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Special Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XOrdinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Sequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XApproximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Number 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.515Alabdulmohsin Ibrahim Mauthttp://id.loc.gov/vocabulary/relators/aut767908BOOK9910300124403321Summability Calculus1563787UNINA