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The bounds for the error term of an asymptotic approximation of Jacobi polynomials. (English) Zbl 0643.41022
Orthogonal polynomials and their applications, Proc. Int. Symp., Segovia/Spain 1986, Lect. Notes Math. 1329, 203-221 (1988).

[For the entire collection see Zbl 0638.00018.]

We consider a new asymptotic approximation of Jacobi polynomials P n (α,β) (cosθ) and we obtain a realistic and explicit bound for the corresponding error term. The approximation is of Hilb’s type and is uniformly valid for 0<θπ-ϵ, ϵ>0. Bounds for the error term in the asymptotic approximation of the zeros of P n (α,β) (cosθ) are also given.


MSC:
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A10Approximation by polynomials