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101 0 $aeng
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181   $ctxt$2rdacontent
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200 10$aSummability Calculus $eA Comprehensive Theory of Fractional Finite Sums /$fby Ibrahim M. Alabdulmohsin
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XIII, 165 p.) 
311   $a3-319-74647-2 
327   $a1 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.
330   $aThis 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.   .
606   $aNumber theory
606   $aFunctions of real variables
606   $aSpecial functions
606   $aDifferential equations
606   $aSequences (Mathematics)
606   $aApproximation theory
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aSpecial Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M1221X
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
606   $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023
615  0$aNumber theory.
615  0$aFunctions of real variables.
615  0$aSpecial functions.
615  0$aDifferential equations.
615  0$aSequences (Mathematics).
615  0$aApproximation theory.
615 14$aNumber Theory.
615 24$aReal Functions.
615 24$aSpecial Functions.
615 24$aOrdinary Differential Equations.
615 24$aSequences, Series, Summability.
615 24$aApproximations and Expansions.
676   $a515
700   $aAlabdulmohsin$b Ibrahim M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767908
906   $aBOOK
912   $a9910300124403321
996   $aSummability Calculus$91563787
997   $aUNINA