The Laguerre Transform.

A novel transform is presented which maps continuum functions such as probability distributions into discrete sequences and permits rapid numerical calculation of convolutions, multiple convolutions, and Neumann expansions for Volterra integral equations. The transform is based on the Laguerre polynomials, associated Laguerre functions, and their convolution properties. Part 1 of this paper deals with functions having support only on 0 infinity. The resulting unilateral Laguerre transform finds applications in convolution of such functions, invercsion of Laplace transform, and in solution to renewal and related Volterra integral equations. Part 2 of this paper deals with functions having support on -infinity, infinity via a bilateral Laguerre transform which is an extension of the unilateral transform. Applications of this technique include convolution of such functions and analysis of the Lindley process. Part 1 has been published in Applied Mathematics and Computation and part 2 has been submitted for publication in that journal. Author