Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 295-306

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

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.


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.