An introduction to Ramanujan’s continued fractions

Abstract

Continued fraction is a method of writing a fraction in a different way. The Rogers-Ramanujan continued fraction is defined as R(q)= ____q1/5_____________ ,|q| less than1 1+ ____q_________ 1+ ____q2________ 1+ ____q3___ 1+……. In his first two letters of G.H.Hardy, and his note book, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fractions. In the year 2000, Bruce C. Provided proof for many of claims about the Roger-Ramanujan and generalized Rogers-Ramanujan continued fractions . found in the lost note book. These fractions are also related to Jigsaw Puzzle problems of dividing a rectangle into squares. Present paper is a conclusive study of Rogers-Ramanujan continued fractions.