$P$--$Q$ "mixed" modular equations of degree 15

Abstract

Ramanujan in his second notebook recorded total of seven $P$--$Q$ modular equations involving theta--function $f(-q)$ with moduli of orders 1, 3, 5 and 15. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving his theta--functions $\phi (q)$ and $\psi (-q)$ with moduli of orders 1, 3, 5 and 15. As a consequence, several values of quotients of theta--function and a continued fraction of order 12 are explicitly evaluated.

References in corpus (1)

• On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions