Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 295-306
doi:10.1155/S1085337504306019

Integral representation of the solutions to Heun's biconfluent equation

S. Belmehdi and J.-P. Chehab

UFR de Mathematiques Pures et Appliquées, Université des Sciencesét Technologies de Lille, Villeneuve d'Ascq Cedex 59655, France

Abstract

First, we trace the genesis of the canonical form of Heun's biconfluent equation. Second, we present a method which allows us to find an integral expression as a solution to our equation, and finally, using the properties of Meijer G-functions, we give an integral representation of a fundamental system of solutions to the biconfluent equation.