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 $\lambda_n$ by a certain quotient of Dedekind eta-functions at the argument $q=exp(-\pi \sqrt{n/3})$. He then recorded a table of several values of $\lambda_n:=\lambda_{n,\,\, 3}$. 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 $\lambda_{n, p}$ at the argument $q=exp(-\pi \sqrt{n/p})$. We establish several interesting and new explicit evaluations for $\lambda_{n,\,\, p}$ using Ramanujan-Weber class invariant, modular equations and mixed-modular equations