31 research outputs found
Some New Modular Equations of Degree 2 Akin to Ramanujan
In this paper, we obtain some new modular equations of degree 2 for the ratios of Ramanujan's theta-function f and also establish the general formulas for their explicit evaluations. As an application, we establish some new modular relations for Ramanujan-Göllnitz-Gordon continued fraction H(q) with H(qn/2), Ramanujan-Selberg continued fraction V(q) with V(qn/2) and Eisenstein continued fraction E(q) with E(qn/2) for n=3, 5 and 7
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
On a new parameter involving Ramanujan's theta-functions
We define a new parameter involving Ramanujan's theta-functions
for any positive real numbers and which is analogous to the parameter
defined by Nipen Saikia \cite{NS1}. We establish some modular
relation involving and to find some explicit values of
. We use these parameters to establish few general theorems for
explicit evaluations of ratios of theta functions involving
On some New Modular Equations and their Applications to Continued Fractions
In this paper, we obtain some new modular equations of degree2. We obtain several general formulas for the explicit evaluations of the Ramanujan's theta{function. As an application, we establish somenew modular relations for Ramanujan{Gollnitz{Gordon continued frac-tion H(q) with H(qn), Ramanujan{Selberg continued fraction V (q)
with V (qn) and Eisenstein continued fraction E(q) with E(qn) for n =6; 10; 14 and 16. We also establish their explicit evaluations
On some new mixed modular equations involving Ramanujan's theta-functions
In his second notebook, Ramanujan recorded altogether 23 P–Q modular equations involving his theta functions. In this paper, we establish several new mixed modular equations
involving Ramanujan’s theta-functions ϕ and ψ which are akin to those recorded in his notebook
Ratios of Ramanujan's Theta Function ψ and Evaluations
In this paper, we establish several new modular equations of degree 9 using Ramanujan's mixed modular equations. We also establish several general formulas for explicit evaluations of ratios of Ramanujan's theta function
On some new modular equations of degree 9 and their applications
In this paper, we establish several new modular equations of degree 9 using Ramanujan's modular equations. We also establish several new general formulas to compute the values for r 9,n and râ² 9. As an application, we establish explicit evaluations of Ramanujan's remarkable product of theta-functions
Schläfli-type mixed modular equations of degrees 1, 3, n and 3n.
In this paper, we establish several new Schlafli-type mixed modular equations of composite degrees. These equations are analogous to those recorded by Ramanujan in his second notebook. As an application, we establish several new explicit values for the Ramanujan-Weber class invariant Gn for n = 12,48,51,57,3/4,3/16,3/17 and 3/19