Generalizations of Ramanujans Continued fractions
arXiv:1107.2393
Abstract
In this article we continue a previous work in which we have generalized the Rogers Ramanujan continued fraction (RR) introducing what we call, the Ramanujan-Quantities (RQ). We use the Mathematica package to give several modular equations for certain cases of Ramanujan Quantities-(RQ). We also give the modular equations of degree 2 and 3 for the evaluation of the first derivative of Rogers-Ramanujan continued fraction. More precicely for certain classes of (RQ)'s we show how we can find the corresponding continued fraction expansions-S, in which we are able to evaluate with numerical methods some lower degree modular equations of this fraction and its derivatives. A systematicaly method for evaluating theoriticaly certain (RQ)'s (not for all) and their derivatives, with functions used by Ramanujan himself, is presented. We give applications and several results.
31 pages, Ramanujan, Continued fractions
References in corpus (4)
- The complete evaluation of Rogers Ramanujan and other continued fractions with elliptic functions
- Integrals related with Rogers Ramanujan continued fraction and q-products
- Jacobian Elliptic Functions, Continued Fractions and Ramanujan Quantities
- The First Derivative of Ramanujans Cubic Continued Fraction