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