Transmutations and irregular singular points

Abstract

We consider transumtations for a class of problems in partial differential equations where the underlying equation, involving two assignable parameters, is an associated ordinary differential equation with an irregular singular point. An integral formula for the solution of this associated problem, valid for negative values of a timelike variable t, permits relating the solution of the problems in partial differential equations to be bounded or slow groth solutions of generalized heat problems. Applications of the formulas are made to Cauchy and boundary type problems.

Keywords:

• Transmutation canchy problem
• irregular singular point
• Hankel function
• Schlömilch function

AMS:

• 35C15
• 34A25