New properties for ramanujan's continued rractions

Abstract

Ramanujan was able to find the factorisation theorem for those two im- portant identities about the Rogers-Ramanujan continued fraction, resulting into new identities. In his notebook, he also wrote the 2- and 5-dissections of the Rogers- Ramanujan continued fraction and its reciprocal. In this thesis, we factorise some identities about Ramanujan's cubic continued fraction analogously to those of the famous Rogers-Ramanujan continued fraction, following the lead of Ramanujan. As applications, we established as corol- laries the early works on Ramanujan's cubic continued fractions. Moreover, we also recorded several new results for Ramanujan's cubic continued fraction and provided a 3-dissection property for (q; q)(q2; q2). Lastly, we proved the 2-dissection of the Göllnitz-Gordon functions.