ZEROS AND STIELTJES CONTINUED FRACTION FOR

L. R. Shenton (U. S. A.) and K. O. Bowman (U. S. A.)

Received August 14, 2008

Abstract

For an orthogonal set of polynomials relating to a kernel weight function, we consider the zeros of focusing attention on the largest. Systems such as binomial in its three forms (Poisson, binomial, negative binomial), the normal, and the approach using a Maple code for zeros of functions expressed in factorial form are described. In some cases a nearly linear form for the largest zero is Particular attention is given to the third degree zeros relating to the general case.

Keywords and phrases: largest zeros, Maple code, orthogonal system, probability models.