Asymptotics and bounds for the zeros of Laguerre polynomials: A survey
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.
scientific article; zbMATH DE number 1787645
scientific article