Interpolation of Entire Functions Associated with Some Freud Weights, II

Abstract

In [J. Approx Theory71 (1992), 123-137], Al-Jarrah and Hasan considered the weight function W(x) = exp(−2 | x |α), α > 0, x ∈ R, and investigated the growth of an entire function ƒ that guarantees the geometric convergence of the Lagrange and Hermite interpolation processes and the Gauss-Jacobi quadrature formula for ƒ and its higher derivatives when the nodes of interpolation are chosen to be the zeros of the orthogonal polynomial associated with W. In this paper, we repeat investigations similar to those of Al-Jarrah and Hasan, but this time with a more general Freud-type weight function Ŵ2(x) = w2(x)exp(−2Q(x)), x ∈ R, where, for example, w(x) is a generalized Jacobi factor, and Q(x) is an even function that satisfies various restrictions.