A PAGE ON EISENSTEIN SERIES IN RAMANUJAN'S LOST NOTEBOOK

Page 188 in Ramanujan's lost notebook is devoted to a certain class of infinite series connected with Euler's pentagonal number theorem. These series are represented in terms of Ramanujan's famous Eisenstein series $P, Q$, and $R$. The purpose of this paper is to prove all the formula...

Full description

Saved in:
Bibliographic Details
Published inGlasgow mathematical journal Vol. 45; no. 1; pp. 123 - 129
Main Authors BERNDT, BRUCE C., YEE, AE JA
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2003
Subjects
11F11
11F11
Online AccessGet full text

Cover

More Information
Summary:Page 188 in Ramanujan's lost notebook is devoted to a certain class of infinite series connected with Euler's pentagonal number theorem. These series are represented in terms of Ramanujan's famous Eisenstein series $P, Q$, and $R$. The purpose of this paper is to prove all the formulas on page 188 and to show that one of them leads to an interesting, new recurrence formula for $\sigma (n)$, the sum of the positive divisors of $n$.
Bibliography:ark:/67375/6GQ-VGQJC3L2-7
PII:S0017089502001076
istex:FE2389529011B56BCDF9E43650D40DBBC80D1B2C
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089502001076