The hypergeometric equation and Ramanujan functions
type: Item
instance of: scholarly article
title: The hypergeometric equation and Ramanujan functions
zbMATH Open document ID: 1072.11052
DOI: 10.1023/B:RAMA.0000012426.23921.24
published in: The Ramanujan Journal
publication date: 2004-05-27T00:00:00Z
review text: 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.
reviewed by: Yilmaz Simsek
Mathematics Subject Classification ID: 11J91
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 37F05
zbMATH DE Number: 2069231
zbMATH Keywords: hypergeometric equation
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: Ramanujan functions
zbMATH Keywords: Modular functions
zbMATH Keywords: nonlinear differential equations
author: Wadim Zudilin
MaRDI profile type: Publication
full work available at URL: b:rama.0000012426.23921.24
OpenAlex ID: W2041628190
description: scientific article; zbMATH DE number 2069231