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Zbl 1008.65011
Gatteschi, Luigi
Asymptotics and bounds for the zeros of Laguerre polynomials: A survey. (English)
[J] J. Comput. Appl. Math. 144, No.1-2, 7-27 (2002). ISSN 0377-0427

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.
[N.M.Temme (Amsterdam)]

MSC 2000:: *65D20 Computation of special functions
33C10 Cylinder functions, etc.
33C45 Orthogonal polynomials and functions of hypergeometric type
33F05 Numerical approximation of special functions

Keywords: Laguerre polynomial; asymptotics of zeros; bounds of zeros; Bessel function; Airy function; Hermite polynomial; Whittaker function; uniform asymptotic approximation; Liouville-Green transform; numerical examples

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