








1. 
Record Nr. 
UNINA9910257378903321 


Autore 
Candelpergher Bernard 


Titolo 
Ramanujan Summation of Divergent Series / / by Bernard Candelpergher 







Pubbl/distr/stampa 


Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 









ISBN 






Edizione 
[1st ed. 2017.] 





Descrizione fisica 

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






Collana 

Lecture Notes in Mathematics, , 00758434 ; ; 2185 






Disciplina 






Soggetti 

Sequences (Mathematics) 
Functions of complex variables 
Number theory 
Sequences, Series, Summability 
Functions of a Complex Variable 
Number Theory 








Lingua di pubblicazione 






Formato 
Materiale a stampa 





Livello bibliografico 
Monografia 





Nota di contenuto 

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. 








Sommario/riassunto 

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 EulerMacLaurin 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. 





 