Hypergeometric equation and Ramanujan functions, Preprint, 2000, submitted for publication [1 citations — 1 self]
Download:
by W. Zudilin, Q Dq
Moscow Lomonosov State University Department of
http://www.mi.uni-koeln.de/~wzudilin/ramanujan.pdf
Add To MetaCart
Abstract:
Abstract. In this paper we give analogues of the Ramanujan functions and nonlin-ear differential equations for them. Investigating a modular structure of solutions for nonlinear differential systems, we deduce new identities between the Ramanujan and hypergeometric functions. Another result of this paper is a solution of transcendence problems concerning nonlinear systems. In 1916 S. Ramanujan has proved [12] that the functions P (q) = 1 − 24 n=1 σ1(n)q n, n=1 Q(q) = 1 + 240 σ3(n)q n ∞�, R(q) = 1 − 504 σ5(n)q n, where σk(n) = � d|n dk, satisfy the system of nonlinear differential equations q dP dq
