Ramanujan summation of divergent series / by Bernard Candelpergher.

Format:

Book

Author/Creator:

Candelpergher, Bernard, Author.

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2185

Language:

English

Subjects (All):

Sequences (Mathematics).

Functions of complex variables.

Number theory.

Sequences, Series, Summability.

Functions of a Complex Variable.

Number Theory.

Local Subjects:

Sequences, Series, Summability.

Functions of a Complex Variable.

Number Theory.

Physical Description:

1 online resource (XXIII, 195 p. 7 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing, AG 2017.

Summary:

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 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. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. 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.

Contents:

Introduction: The Summation of Series

1 Ramanujan Summation

3 Properties of the Ramanujan Summation

3 Dependence on a Parameter

4 Transformation Formulas

5 An Algebraic View on the Summation of Series

6 Appendix

7 Bibliography

8 Chapter VI of the Second Ramanujan's Notebook.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783319636306

3-319-63630-8

OCLC:

1004663268