A non-trivial special case of the biconfluent Heun equation [0,1,1_3]: orthogonality of its solutions

Abstract

A special case of the biconfluent Heun equation which is not reducible to a form of a hypergeometric equation is solved by means of a Laplace transform. The solutions are double series which exhibit a type of orthogonality comparable in some respects to that of Fourier-Bessel type.