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 |  | 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 | doi | https://doi.org/10.1007/978-3-319-74648-7 | isbn_softcover | 978-3-319-74647-0 | isbn_ebook | 978-3-319-74648-7 | copyright | Springer International Publishing AG, part of Springer Nature 2018 |
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