COMPANION PRODUCT RELATIONS FOR HERMITE TYPE POLYNOMIALS,
Abstract
There is a treatment of formulas related to the polynomials H sub p, k(x), p an integer and p greater than or equal to 2. When p=2, these are the classical Hermite polynomials. There are formulas for (1) expressing the product H sub p,m (x)H sub p,n (x) as a sum of such polynomials and for (2) expressing the polynomial H sub p,m+n (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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1963
- Accession Number
- AD0420346
Entities
People
- L. R. Bragg
Organizations
- University of Wisconsin–Madison