Algorithms for classical orthogonal polynomials
| dc.creator | Koepf, Wolfram | |
| dc.creator | Schmersau, Dieter | |
| dc.date | 1996-12-05 | |
| dc.date.accessioned | 2026-07-07T09:15:41Z | |
| dc.date.available | 2026-07-07T09:15:41Z | |
| dc.description | In 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.identifier | https://arxiv.org/abs/math/9612224 | |
| dc.identifier | http://arxiv.org/abs/math/9612224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153100 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Algorithms for classical orthogonal polynomials | |
| dc.type | text |