The Christoffel function for the Hermite weight is bell-shaped

Abstract

We show that the Christoffel function l n associated with the Hermite weight function w H ðxÞ ¼ expðÀx 2 Þ is bell-shaped. As a consequence, we describe completely how the weights in a Gauss-type quadrature formula associated with w H ðxÞ are arranged in magnitude. r

The impact of constellation cardinality on Gaussian channel capacity

“…Due to the symmetry of the Hermite polynomials, X Q m is also symmetric, with a bell-shaped distribution [11]. For each odd m, there is an atom at zero.…”