Algorithms for classical orthogonal polynomials

dc.creatorKoepf, Wolfram
dc.creatorSchmersau, Dieter
dc.date1996-12-05
dc.date.accessioned2026-07-07T09:15:41Z
dc.date.available2026-07-07T09:15:41Z
dc.descriptionIn this article explicit formulas for the recurrence equation p_{n+1}(x) = (A_n x + B_n) p_n(x) - C_n p_{n-1}(x) and the derivative rules sigma(x) p'_n(x) = alpha_n p_{n+1}(x) + beta_n p_n(x) + gamma_n p_{n-1}(x) and sigma(x) p'_n(x) = (alpha_n-tilde x + beta_n-tilde) p_n(x) + gamma_n-tilde p_{n-1}(x) respectively which are valid for the orthogonal polynomial solutions p_n(x) of the differential equation sigma(x) y''(x) + r(x) y'(x) + lambda_n y(x) = 0 of hypergeometric type are developed that depend only on the coefficients sigma(x) and tau(x) which themselves are polynomials w.r.t. x of degree not larger than 2 and 1, respectively. Partial solutions of this problem had beed previously published by Tricomi, and recently by Yáñez, Dehesa and Nikiforov.
dc.identifierhttps://arxiv.org/abs/math/9612224
dc.identifierhttp://arxiv.org/abs/math/9612224
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153100
dc.subjectClassical Analysis and ODEs
dc.titleAlgorithms for classical orthogonal polynomials
dc.typetext

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