Ramanujan Summation of Divergent Series

• Main Author: Candelpergher, Bernard (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Lecture Notes in Mathematics, 2185
• Subjects: Mathematics.; Functions of complex variables.; Sequences (Mathematics).; Number theory.; Sequences, Series, Summability.; Functions of a Complex Variable.; Number Theory.

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 funct...

Table of 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.