New identities for ratios of ramanujan's theta function

Ramanujan in his notebooks, has established several new modular equation which he denoted as P and Q. In this paper, we establish several new identities for ratios of Ramanujan's theta function involving �(q). We establish some new explicit evaluations for the ratios of Ramanujan's theta function. We also establish some new modular relations for a continued fraction of order twelve II(q) with H(qn) for n =2, 4, 6, 8, 10. 12. 14 and 16

Some modular equations in the form of schlaafli1

On page 90 of his first notebook, S. Ramanujan records Schlaa i-type modular equations for degrees 3, 5, 7, 11, 13, 17 and 19. In this paper, we establish Schlaa i-type modular equations for degrees 11, 13, 17 and 19 which are recorded by Ramanujan in his first notebook. We also establish several new Schlaa i-type modular equations of degrees 2, 4, 9, 15, 23, 25, 29, 31, 47 and 71. As an application, we deduce some explicit evaluations of Ramanujan-Weber class invariants

On some Ramanujan-Selberg continued fraction.

On page 55 of his `lost' notebook, Ramanujan has recorded several P-Q eta-function identities with two moduli. In this paper, we establish several P-Q modular equations of degree 4. We also establish modular relations and explicit evaluations of Ramanujan-Selberg continued fraction

General formulas for explicit evaluations of Ramanujan's cubic continued fraction

On page 366 of his lost notebook 15, Ramanujan recorded a cubic contin- ued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V (q 3) and also establish some explicit evaluations using the values of remarkable product of theta-function

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