The hypergeometric equation and Ramanujan functions (Q1430277)

There are 4 sections in this paper. The author gives the history of the Ramanujan functions and related topics. Ramanujan functions satisfy a system of nonlinear differential equations. This paper deals with both nonlinear systems satisfied by modular functions and identities between these functions and hypergeometric functions for a special choice of parameters. The author gives some examples related to these functions and analogues of the Ramanujan functions and nonlinear differential equations for them. He investigates a modular structure of solutions for nonlinear differential systems. He finds identities between the Ramanujan functions and hypergeometric functions. He also gives a solution of transcendence problems concerning nonlinear systems, which is given by the table explicitly.