Ramanujan Summation of Divergent Series

Bernard Candelpergher (Autor)

Buch | Softcover

XXIII, 195 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-63629-0 (ISBN)

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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.

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.

Erscheinungsdatum	21.10.2017
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XXIII, 195 p. 7 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	340 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Borel summation • Calculus & mathematical analysis • Calculus & mathematical analysis • Complex analysis, complex variables • Divergent • Euler-MacLaurin formula • Euler Summation • Functions of a Complex Variable • Mathematics • mathematics and statistics • Number Theory • Ramanujan • Sequences, Series, Summability • series • Summation
ISBN-10	3-319-63629-4 / 3319636294
ISBN-13	978-3-319-63629-0 / 9783319636290
Zustand	Neuware