Explicit evaluations of a level 13 analogue of the Rogers-Ramanujan continued fraction

The Rogers-Ramanujan continued fraction has a representa-tion as an infinite product given byq1/5∏j=1∞(1−qj)(j5) where |q|<1 and (jp) is the Legendre symbol. In his letters to Hardy and in his notebooks, Ramanujan recorded some exact numerical values of the Rogers-Ramanujan continued fraction for specific values of q. In this work, we give explicit evaluations of the level 13 analogue defined byq∏j=1∞(1−qj)(j13).