Algorithms for classical orthogonal polynomials
  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 Y\'a\~nez, Dehesa and Nikiforov. 
Wolfram Koepf, Dieter Schmersau