Journal article
On co-recursive orthogonal polynomials and their application to potential scattering
Journal of Mathematical Analysis and Applications, Vol.136(1), pp.1-19
1988
Abstract
Let {Pn(x)}n = 0 ∞ be a system of polynomials, orthogonal with respect to a positive-definite moment functional and satisfying the recurrence relation Pn(x) = (x - cn)Pn - 1(x) + λnPn - 2(x), n = 1, 2,..., where P0(x) = 1 and P-1(x) = 0. The corresponding co-recursive orthogonal polynomials {Pn *(x)}n = 0 ∞ satisfy the same recurrence relations except for n = 1, where now P1 *(x) = αx - c1 - β, α ≠ 0, and P0 *(x) = 1. The Pn * are orthogonal with respect to a moment functional which is positive-definite for α > 0 and quasi-definite for α < 0. The properties of the Pn *(x) (separation theorems, true interval of orthogonality, etc.) can be determined from those of the Pn(x). These polynomials occur in the L2-solution of the radial Schrödinger equation for a separable potential, where Pn(x) is the Tchebichef polynomial of the second kind in the case of S-waves.
Details
- Title
- On co-recursive orthogonal polynomials and their application to potential scattering
- Authors/Creators
- H.A. Slim (Author/Creator) - Murdoch University
- Publication Details
- Journal of Mathematical Analysis and Applications, Vol.136(1), pp.1-19
- Publisher
- Academic Press Inc.
- Identifiers
- 991005542710607891
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
Metrics
33 Record Views
InCites Highlights
These are selected metrics from InCites Benchmarking & Analytics tool, related to this output
- Citation topics
- 9 Mathematics
- 9.270 Functional Analysis
- 9.270.1218 Orthogonal Polynomials
- Web Of Science research areas
- Mathematics
- Mathematics, Applied
- ESI research areas
- Mathematics