A FORMULA OF HILB TYPE FOR ORTHOGONAL POLYNOMIALS

[摘要] Let (P(n)(alpha))n is-an-element-of N0 be the ultraspherical polynomials normalized by P(n)(alpha)(1) = 1, and let (P(n))n is-an-element-of N0 be a further sequence of orthogonal polynomials satisfying a three-term recurrence relation which is-up to a small perturbation-equal to that of the P(n)(alpha). We give estimations for \P(n)(cos theta) - P(n)(alpha)(cos theta)\ for small theta and large n. Using the classical formula of Hilb's type, this leads to a Hilb-type formula for the polynomials P(n). This result has consequences in probability theory.

[发布日期] 1993-12-31

[关键词] ULTRASPHERICAL POLYNOMIALS;BESSEL FUNCTIONS;ASYMPTOTIC OF ORTHOGONAL POLYNOMIALS