Electrostatic interpretation for the zeros of certain polynomials and the Darboux process

[摘要] The purpose of this paper is to extend the electrostatic interpretation of Stieltjes to the zeros of a larger class of important polynomials. To keep things simple I consider polynomials that are obtained from those considered by Stieltjes by means of the so-called Darboux process applied to the difference operator featuring in their three term recursion relation. It will rum out that some of the beauty in the results of Stieltjes is preserved in this process. It would be interesting to interpret the Darboux process at the electrostatic level and this paper gives experimental data that might help in this direction. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] electrostatic interpretation;Stieltjes;zeros of polynomials;Darboux process