3 research outputs found
A modular transformation for a generalized theta function with multiple parameters
We obtain a modular transformation for the theta function, which enables us to unify and extend several modular transformations known in literature. © 2010 Springer Science+Business Media, Inc
On some remarkable product of theta-function
On pages 338 and 339 in his first notebook, Ramanujan records eighteen values for a certain product of theta-function. All these have been proved by B. C. Berndt, H. H. Chan and L-C. Zhang 4. Recently M. S. Mahadeva Naika and B. N. Dharmendra. 7, 8 and Mahadeva Naika and M. C. Maheshkumar 9 have obtained general theorems to establish explicit evaluations of Ramanujan's remarkable product of theta-function. Following Ramanujan we define a new function bM, N as defined in (1.5). The main purpose of this paper is to establish some new general theorems for explicit evaluations of product of theta-function. © 2008 Austral Internet Publishing. All rights reserved
Certain quotient of eta-function identities.
On page 212 in his lost notebook, Ramanujan defined a parameter by a certain quotient of Dedekind eta-functions at the argument . He then recorded a table of several values of . All these have been established by B. C. Berndt, H. H. Chan, S.-Y. Kang and L.-C. Zhang \cite{BCB4}. In this paper following Ramanujan we defined a parameter at the argument . We establish several interesting and new explicit evaluations for using Ramanujan-Weber class invariant, modular equations and mixed-modular equations