A new solution of the biconfluent Heun equation

Abstract

The Laplace transform and inverse are applied to a soluble system of differential equations to deduce an explicit solution of the biconfluent Heun equation wich has not previously been mentioned in the literature. This is presented in the form of a triple convergent series of hypergeometric type. The computer algebra package MAPLE V is used deal with an ancillary system of non-linear algebraic equation.

Keywords

• biconfluent
• heun
• hypergeometric