Rao coefficients for the solution of convolution integral equations (Q1573068)

For the solution \(h(x)\) of the convolution integral equation \(f = h\ast g,\) given the kernel function \(g(x)\) and the convolution function \(f(x),\) \textit{J.~S.~Rao} [Proc. Indian Acad. Sci., Sect. A 65, 233-239 (1967; Zbl 0147.10602)] derived a useful expression \(h(x) =\sum_n a_nf^{(n)}(x)\) in terms of recursively defined coefficients \(a_n.\) In this paper, these coefficients are explicitly evaluated up to order \(n = 20\) in terms of moments of \(g(x).\) The software Maple is used to produce general expressions for the higher even order Rao coefficients, and numerical values of \(a_n\) for two forms of the Gaussian distribution.