Two theta-function identities for the Ramanujan-Selberg continued fraction and applications

摘要

We prove two theta-function identities for the Ramanujan-Selberg continued fraction which are analogous to those of the Rogers-Ramanujan continued fraction. These identities are then used to prove reciprocity formulas and general theorems for the explicit evaluations of the Ramanujan-Selberg continued fraction. (C) 2015 Elsevier Inc. All rights reserved.