The calculation of multidimensional Hermite polynomials and Gram-Charlier coefficients

Abstract

The paper documents derivations of: (a) a recurrence relation for calculating values of multidimensional Hermite polynomials, (b) a recurrence relation for calculating an approximation to the Gram-Charlier coefficients of the probability density distribution associated with a random process, based on (a), (c) an efficient algorithm to utilize the formulae in (a) and (b).