The Laguerre transform of product of functions

The Laguerre transform developed by Keilson, Nunn and Sumita provides an algorithmic basis for mechanizing various continuum operations such as multiple convolutions, integration, differentiation, and multiplication by polynomials and exponential functions. This paper develops a numerical procedure for finding the Laguerre coefficients of a product of functions in terms of the Laguerre coefficients of individual functions. The procedure enables one to evaluate multiple convolutions and other continuum operations described above even when product form functions are involved, thereby further enhancing the power of the Laguerre transform.