Generating differential equations satisfied by products of functions Original Research Article

Based on the coefficients of two homogeneous linear differential equations, a method is proposed to construct a third homogeneous linear differential equations which is satisfied by all products of the form uv, where u and v satisfy, respectively, the first and the second given differential equation. The method was used recently in the computation of rapidly oscillatory integrals with kernels which are products of Bessel functions and their variants.