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Summability Calculus - A Comprehensive Theory of Fractional Finite Sums (Paperback, 1st ed. 2018)
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Summability Calculus - A Comprehensive Theory of Fractional Finite Sums (Paperback, 1st ed. 2018)
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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.
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