Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 169050, 14 pages
http://dx.doi.org/10.5402/2012/169050
Research Article

A Parameter for Ramanujan's Function χ(q): Its Explicit Values and Applications

Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, India

Received 3 May 2012; Accepted 28 June 2012

Academic Editors: L. Hajdu, L. S. Heath, and H. J. Ruskin

Copyright © 2012 Nipen Saikia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define a new parameter 𝐼 π‘˜ , 𝑛 involving quotient of Ramanujan's function πœ’ ( π‘ž ) for positive real numbers π‘˜ and 𝑛 and study its several properties. We prove some general theorems for the explicit evaluations of the parameter 𝐼 π‘˜ , 𝑛 and find many explicit values. Some values of 𝐼 π‘˜ , 𝑛 are then used to find some new and known values of Ramanujan's class invariant 𝐺 𝑛 .