Ramanujan Summation of Divergent Series Candelpergher Bernard
Ramanujan Summation of Divergent Series Candelpergher Bernard The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second…
Specifikacia Ramanujan Summation of Divergent Series Candelpergher Bernard
Ramanujan Summation of Divergent Series Candelpergher Bernard
The 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 provides simple proofs of theorems on the summation of some divergent series. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions.
For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. Several examples and applications are given. The relation with other summation processes such as those 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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