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.
