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Summability calculus = a comprehensi...

Alabdulmohsin, Ibrahim M.

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Summability calculus = a comprehensive theory of fractional finite sums /

紀錄類型:	書目-電子資源 : 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.
內容註:	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.
Contained By:	Springer eBooks
標題:	Fractional calculus. -
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:

898980
Fractional calculus.

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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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 Fractional calculus. $3 898980
650 0 $a Mathematical analysis. $3 516833
650 0 $a Finite differences. $3 587824
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Real Functions. $3 891265
650 2 4 $a Special Functions. $3 897326
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Sequences, Series, Summability. $3 897266
650 2 4 $a Approximations and Expansions. $3 897324
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-74648-7
950 $a Mathematics and Statistics (Springer-11649)