Ramanujan Continued Fractions for Products of Gamma-Functions
We use continuous relations for the generalised hypergeometric series 3F2 to give new proofs of three of Ramanujan′s elegant continued fractions for products and quotients of gamma functions. Previous proofs were somewhat ad hoc and did not show any connections with hypergeometric functions.
Zhang, Liang-Chen. "Ramanujan continued fractions for products of gamma-functions." Journal of mathematical analysis and applications 174, no. 1 (1993): 22-52.
Journal of Mathematical Analysis and Applications