RAMANUJAN’S CUBIC CONTINUED FRACTION AND RELATED RESULTS

Abstract

On page 366 of his lost notebook [3], Ramanujan recorded a continued fraction known as Ramanujan’s Cubic Continued Fraction  defined as

 

He also claimed that there are many results of  that are analogous to , Rogers-Ramanujan Continued Fraction.  and it’s other results are recorded in [2, 345-347] and [1, section 3.3] of his lost notebook. ^ In this paper we derive some new identities involving Ramanujan’s Cubic continued fraction  by using Ramanujan’s theta function.