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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 873078, 10 pages
http://dx.doi.org/10.1155/2012/873078
Research Article

Approximate Closed-Form Formulas for the Zeros of the Bessel Polynomials

Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana, 58060 Morelia, MN, Mexico

Received 11 June 2012; Revised 10 September 2012; Accepted 23 September 2012

Academic Editor: Stefan Samko

Copyright © 2012 Rafael G. Campos and Marisol L. Calderón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We find approximate expressions and for the real and imaginary parts of the th zero of the Bessel polynomial . To obtain these closed-form formulas we use the fact that the points of well-defined curves in the complex plane are limit points of the zeros of the normalized Bessel polynomials. Thus, these zeros are first computed numerically through an implementation of the electrostatic interpretation formulas and then, a fit to the real and imaginary parts as functions of , and is obtained. It is shown that the resulting complex number is -convergent to for fixed .