Approximate closedform formulas for the zeros of the Bessel Polynomials
Abstract
We find approximate expressions x(k,n) and y(k,n) for the real and imaginary parts of the kth zero z_k=x_k+i y_k of the Bessel polynomial y_n(x). To obtain these closedform formulas we use the fact that the points of welldefined 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 k and n is obtained. It is shown that the resulting complex number x(k,n)+i y(k,n) is O(1/n^2)convergent to z_k for fixed k
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 arXiv:
 arXiv:1105.0957
 Bibcode:
 2011arXiv1105.0957C
 Keywords:

 Mathematical Physics;
 33C47;
 33F05;
 33C10;
 30C15
 EPrint:
 9 pages, 2 figures