Baratella, Paola; Gatteschi, Luigi 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 \(P_ n^{(\alpha,\beta)}(\cos \theta)\) 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 \(0<\theta \leq \pi -\epsilon\), \(\epsilon >0\). Bounds for the error term in the asymptotic approximation of the zeros of \(P_ n^{(\alpha,\beta)}(\cos \theta)\) are also given. Cited in 1 ReviewCited in 6 Documents MSC: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 41A10 Approximation by polynomials Keywords:asymptotic approximation; Jacobi polynomials; error term Citations:Zbl 0638.00018 PDFBibTeX XML Digital Library of Mathematical Functions: §18.15(i) Jacobi ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials §18.15(i) Jacobi ‣ §18.15 Asymptotic Approximations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials