On some explicit evaluations of the ratios of Ramanujan's theta-function.

In this paper, we establish several new modular equations of degree 9 using Ramanujan’s modular equations. We also establish several general formulas for explicit evaluations of h9,n, h0 9,n, l9,n and l 0 9,n. As an application, we establish some explicit evaluations for Ramanujan’s cubic continued fraction

New identities for Ramanujan's cubic continued fraction.

In this paper, we present some new identities providing relations between Ramanujan's cubic continued fraction V(q)V(q) and the other three continued fractions V(q9)V(q9), V(q17)V(q17) and V(q19)V(q19). In the process, we establish some new modular equations for the ratios of Ramanujan's theta functions. We also establish some general formulas for the explicit evaluations of ratios of Ramanujan's theta functions

On some new identities for Ramanujan's cubic continued fraction.

In this paper, we establish some new modular relations connecting Ramanujan's cubic continued fraction V (q) with V(qn), for n= 4, 6, 8,10, 12, 14, 16 and 22

On some new Schläfli-type mixed modular equations

On pages 86 and 88 of his first notebook, Ramanujan recorded eleven Schl\"{a}fli-type modular equations for composite degrees. Out of eleven, ten have been proved by Berndt using theory of modular forms. In this paper, we establish several new Schl\"{a}fli-type mixed modular equations

A continued fraction of order 4 found in Ramanujan's `lost' notebook.

On page 44 of his lost notebook, Ramanujan has recorded many continued fractions of orders 4, 5, 6 and 8. In this paper, we establish several interesting results of a continued fraction of order 4 which are analogous to Rogers-Ramanujan and cubic continued fractions

Certain identities for a continued fraction of Ramanujan.

Ramanujan has recorded several continued fractions in his notebooks. In this paper, we establish several identities of a continued fraction of Ramanujan $V(q)$. We also establish several relations between $V(q)$ and $V(q^n)$ and several explicit evaluations of $V(q)$

Women letter-writing and the life of the mind in England c. 1650-1750

EThOS - Electronic Theses Online ServiceGBUnited Kingdo