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
UFR de Mathematiques Pures et Appliquées, Université des Sciencesét Technologies de Lille, Villeneuve d'Ascq Cedex 59655, France
Received 1 October 2002
Copyright © 2004 S. Belmehdi and J.-P. Chehab. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.