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Asymptotics and bounds for the zeros of Laguerre polynomials: A survey. (English) Zbl 1008.65011
The zeros of the Laguerre polynomial $L_n^{(\alpha)}(x)$ are considered for large values of the quantity $\nu=4n+2\alpha+2$, including the cases when one or both parameters $n$ and $\alpha$ are large. An overview is given for bounds and for asymptotic approximations of the zeros. New uniform approximations are given in terms of zeros of a Bessel function and of the Airy function. Numerical results and graphical comparisons are provided.

65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
33C45Orthogonal polynomials and functions of hypergeometric type
33F05Numerical approximation and evaluation of special functions
Full Text: DOI
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