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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.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xiii, 165 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Mathematical analysis. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-74648-7
ISBN:	9783319746487

Summability calculus = a comprehensive theory of fractional finite sums /
Alabdulmohsin, Ibrahim M.

Summability calculusa comprehensive theory of fractional finite sums /[electronic resource] :by Ibrahim M. Alabdulmohsin. - Cham :Springer International Publishing :2018. - xiii, 165 p. :ill., digital ;24 cm.

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:

527926
Mathematical analysis.

LC Class. No.: QA303.2 / .A433 2018

Dewey Class. No.: 515

Summability calculus = a comprehensive theory of fractional finite sums /
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245 1 0 $a Summability calculus $h [electronic resource] : $b a comprehensive theory of fractional finite sums / $c by Ibrahim M. Alabdulmohsin.
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300 $a xiii, 165 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Mathematical analysis. $3 527926
650 0 $a Fractional calculus. $3 677227
650 0 $a Finite differences. $3 528594
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650 2 4 $a Number Theory. $3 672023
650 2 4 $a Real Functions. $3 672094
650 2 4 $a Special Functions. $3 672152
650 2 4 $a Ordinary Differential Equations. $3 670854
650 2 4 $a Sequences, Series, Summability. $3 672022
650 2 4 $a Approximations and Expansions. $3 672153
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-74648-7
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