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On co-recursive orthogonal polynomials and their application to potential scattering

Slim, H.A. (1988) On co-recursive orthogonal polynomials and their application to potential scattering. Journal of Mathematical Analysis and Applications, 136 (1). pp. 1-19.

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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.

Item Type: Journal Article
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Publisher: Academic Press Inc.
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