A General Expression for Hermite Expansions with Applications

Hermite polynomials arise when dealing with functions of normally distributed variables, and are commonly thought as the analog simple on regular variables. Therefore expansion should be an Taylor expansion. Indeed there is a strong connection between two – general coefficient in weighted integral nth derivative, compared to derivative evaluated at zero case Taylor. This fact can used derive for function. Furthermore, it provides method providing proofs many identities. expansions normal probability distribution function, cumulative function indicator Finally, algorithm numerically perform presented, which efficient sense that only requires single call quadrature method.