On the Siegel conjecture for second-order homogeneous linear differential equations
type: Item
instance of: scholarly article
title: On the Siegel conjecture for second-order homogeneous linear differential equations
zbMATH Open document ID: 1062.34096
DOI: 10.1023/B:MATN.0000023333.36063.12
author: V. A. Gorelov
published in: Mathematical Notes
publication date: 2004-12-06T00:00:00Z
review text: The paper deals with an investigation of a class of entire analytic functions (so-called \(E\)-functions), satisfying systems of linear differential equations from \(\mathbb{C}(z)\). Siegel conjectured that any \(E\)-function can be represented as a polynomial with suitable algebraic coefficients. In the present paper, it is proved that an \(E\)-function satisfies a second-order homogeneous linear differential equation with coefficients from \(\mathbb{C}(z)\) if and only if it is of a special form, which is described explicitly.
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 30D10
Mathematics Subject Classification ID: 34M25
zbMATH DE Number: 2121383
zbMATH Keywords: \(E\)-functions
zbMATH Keywords: Siegel method
zbMATH Keywords: second-order homogeneous linear differential equations
zbMATH Keywords: Kummer functions
reviewed by: J. Saurer
MaRDI profile type: Publication
Wikidata QID: Q123150627
full work available at URL: b:matn.0000023333.36063.12
OpenAlex ID: W2057076428
description: scientific article; zbMATH DE number 2121383