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Zbl 1072.11052
Zudilin, W.
(Zudilin, V.)
The hypergeometric equation and Ramanujan functions. (English)
[J] Ramanujan J. 7, No. 4, 435-447 (2003). ISSN 1382-4090; ISSN 1572-9303/e

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.
[Yilmaz Simsek (Antalya)]

MSC 2000:: *11J91 Transcendence theory of other special functions
11F03 Modular and automorphic functions
33C05 Classical hypergeometric functions
37F05 Relations and correspondences

Keywords: hypergeometric equation; hypergeometric functions; Ramanujan functions; Modular functions; nonlinear differential equations

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