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Titlebook: Summability Calculus; A Comprehensive Theo Ibrahim M. Alabdulmohsin Book 2018 Springer International Publishing AG, part of Springer Nature

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书目名称Summability Calculus
副标题A Comprehensive Theo
编辑Ibrahim M. Alabdulmohsin
视频video
概述The first book in the literature, which is devoted to fractional finite sums as an object of study on its own right.Unifies many disparate historical results in the works of prominent mathematicians,
图书封面Titlebook: Summability Calculus; A Comprehensive Theo Ibrahim M. Alabdulmohsin Book 2018 Springer International Publishing AG, part of Springer Nature
描述.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..
出版日期Book 2018
关键词Fractional Finite Sums; Analytic Summability Theory; Divergent Series; Special Functions; Finite Differe
版次1
doihttps://doi.org/10.1007/978-3-319-74648-7
isbn_softcover978-3-319-74647-0
isbn_ebook978-3-319-74648-7
copyrightSpringer International Publishing AG, part of Springer Nature 2018
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The Language of Finite Differences, to the Shannon-Nyquist sampling theorem. Finally, we derive many identities that relate to the Euler constant, the Riemann zeta function, the Gregory coefficients, and the Cauchy coefficients, among others.
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Book 2018 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 inte
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Introduction,tend the domains of existing systems and operations consistently, while still preserving as many prior results as possible. In this chapter, we look into the question of how to generalize discrete finite sums and products from the set of integers into the entire complex plane, which give rise to the
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Analytic Summability Theory,nce. It addresses methods of assigning natural values to divergent sums, whose prototypical examples include the Abel summation method, the Cesaro means, and the Borel summability method. As will be established in subsequent chapters, the theory of summability of divergent series is intimately conne
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