On the asymptotic distribution of the zeros of Hermite, Laguerre, and Jonquière polynomials (Q1093834)

The author presents an alternative derivation of the contracted zero distribution of the Hermite and Laguerre polynomials. He also derives the zero distribution of the Jonquière polynomials, \(P_ n(z)\), defined by \(P_ n(z):= (1-z)^ n\sum^{\infty}_{j=1}j^ nz^ j,\) \(n=1,2,3,... \). \(P_ n(z)\) is a polynomial of degree n, having n simple zeros in (- \(\infty,0]\). Some other generalisations of Jonquière polynomials are also considered.