The Rogers–Ramanujan continued fraction and its level 13 analogue

One of the properties of the Rogers–Ramanujan continued fraction is its representation as an infinite product given by (q)=q1/5∏j=1∞(1−qj)(j5) where (jp) is the Legendre symbol. In this work we study the level 13 function R(q)=q∏j=1∞(1−qj)(j13) and establish many properties analogous to those for the fifth power of the Rogers–Ramanujan continued fraction. Many of the properties extend to other levels ℓℓ for which ℓ−1ℓ−1 divides 24, and a brief account of these results is included.