Uniform multi - parameter limit transitions in the Askey tableau

1. Elementary limit formulas We consider the classical orthogonal polynomials as monic polynomials pn(x) = x + terms of degree less than n. We have • Jacobi polynomials p (α,β) n (x) with respect to weight function (1 − x) (1 + x) on (−1, 1); • Laguerre polynomials ln(x) with respect to weight function e −x x on (0,∞); • Hermite polynomials hn(x) with respect to weight function e −x on (−∞,∞). Note that, for α → ∞, the rescaled Jacobi weight function (1−x/α) on (−α 1