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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