An asymptotic representation of the zeros of ultraspherical polynomials. (Italian. English summary) Zbl 0796.33006

Pittaluga, Giovanna

Atti Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat. 117, No. 4-6, 179-190 (1983).

Summary: An asymptotic expansion for the zeros of the \(n\)th degree ultraspherical polynomial \(P^{(\lambda)}_ n(x)\) in terms of the powers of \({1\over n(n+2\lambda)}\) is given. Some examples demonstrate the ability of the expansion for some values of \(\lambda\) and \(n\).

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
65D20	Computation of special functions and constants, construction of tables