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Summability Calculus = A Comprehensi...
~
Alabdulmohsin, Ibrahim M.
Summability Calculus = A Comprehensive Theory of Fractional Finite Sums /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Summability Calculus/ by Ibrahim M. Alabdulmohsin.
其他題名:
A Comprehensive Theory of Fractional Finite Sums /
作者:
Alabdulmohsin, Ibrahim M.
面頁冊數:
XIII, 165 p.online resource. :
Contained By:
Springer Nature eBook
標題:
Number theory. -
電子資源:
https://doi.org/10.1007/978-3-319-74648-7
ISBN:
9783319746487
Summability Calculus = A Comprehensive Theory of Fractional Finite Sums /
Alabdulmohsin, Ibrahim M.
Summability Calculus
A Comprehensive Theory of Fractional Finite Sums /[electronic resource] :by Ibrahim M. Alabdulmohsin. - 1st ed. 2018. - XIII, 165 p.online resource.
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. .
ISBN: 9783319746487
Standard No.: 10.1007/978-3-319-74648-7doiSubjects--Topical Terms:
527883
Number theory.
LC Class. No.: QA241-247.5
Dewey Class. No.: 512.7
Summability Calculus = A Comprehensive Theory of Fractional Finite Sums /
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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.
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