Titlebook: Ramanujan Summation of Divergent Series; Bernard Candelpergher Book 2017 Springer International Publishing AG 2017 Ramanujan.Divergent.Ser

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Book 2017those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.

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0075-8434 ifying the most important summation processes.Only little baThe aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here exten

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Transformation Formulas,on we examine the Borel summability of the series deduced from the Euler-MacLaurin formula. In the second section we use finite differences and Newton series to give a convergent version of the Ramanujan summation which generalizes the classical Laplace-Gregory formula. In the third section we use t

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An Algebraic View on the Summation of Series, is the shift property which seems very strange for a summation procedure. Thus it is necessary to define a general algebraic formalism to unify the Ramanujan summation and the classical methods of summation of series.

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0075-8434 theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.978-3-319-63629-0978-3-319-63630-6Series ISSN 0075-8434 Series E-ISSN 1617-9692

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