Some New Explicit Values of Quotients of Theta-Function ϕ(q)‎ and Applications to Ramanujan's Continued Fractions

Abstract EN

We find some new explicit values of the parameter hk,n for positive real numbers k and n involving Ramanujan's theta-function ϕ(q) and give some applications of these new values for the explicit evaluations of Ramanujan's continued fractions.

In the process, we also establish two new identities for ϕ(q) by using modular equations.