# Accession Number:

## AD0420346

# Title:

## COMPANION PRODUCT RELATIONS FOR HERMITE TYPE POLYNOMIALS,

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1963-07-01

# Pagination or Media Count:

## 18.0

# Abstract:

There is a treatment of formulas related to the polynomials H sub p, kx, p an integer and p greater than or equal to 2. When p2, these are the classical Hermite polynomials. There are formulas for 1 expressing the product H sub p,m xH sub p,n x as a sum of such polynomials and for 2 expressing the polynomial H sub p,mn x as a sum of products of such polynomials, taken two at a time, in which at least one of the polynomials does not have degree exceeding m and the other does not have degree exceeding n. Two sets of generalizations of these for arbitrary p are developed, the sums being formed over the lattice points of a simplex. A by-product of this is a curious combinatorial identity that permits the reduction of certain sums of products of binomial coefficients to simpler form. Author