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Summability calculusa comprehensive ...

Alabdulmohsin, Ibrahim M.

Summability calculusa comprehensive theory of fractional finite sums /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Summability calculusby 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$q(electronic bk.)

Summability calculusa 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$q(electronic bk.)

Standard No.: 10.1007/978-3-319-74648-7doiSubjects--Topical Terms:

186133
Mathematical analysis.

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

Dewey Class. No.: 515

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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 186133
650 0 $a Fractional calculus. $3 208302
650 0 $a Finite differences. $3 190850
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650 2 4 $a Real Functions. $3 273779
650 2 4 $a Special Functions. $3 274846
650 2 4 $a Ordinary Differential Equations. $3 273778
650 2 4 $a Sequences, Series, Summability. $3 275704
650 2 4 $a Approximations and Expansions. $3 281039
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