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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE