M. G. de Bruin, E. B. Saff and R. S. Varga, On the zeros of generalized Bessel polynomials, I, II, Indag. Math. 43 (1981), 1--13; 14--27.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....what the appropriate constraint should be. In general the normalized zeros of a Bessel polynomial approach a smooth curve Gamma in the complex plane, which is symmetric with respect to the horizontal axis [14, Theorem 10 in Chapter 10] The analytic representation of this curve is known [36] [7], hence a possible constraint would be that the charges need to be located at points z i which, after normalization, are in the neighborhood of this curve Gamma. In [43] it was pointed out that the electrostatic interpretation of zeros of orthogonal polynomials indirectly leads to Fekete s ....

M. G. de Bruin, E. B. Saff and R. S. Varga, On the zeros of generalized Bessel polynomials, I, II, Indag. Math. 43 (1981), 1--13; 14--27.

....can be stated as Theorem 3. Under the hypothesis of (2.3) of Theorem 1, dist h Phi z n j ; j (k) Psi n j k=1 n C ffi;oe j ; D oe j ;n j j i = O 1 (n j j ) 2 (j 1) 2.10) We remark that a special case of (2. 10) of Theorem 3 was previously established in de Bruin et al. [5]. Specifically, for the case oe = 1 and n j odd for all j 1 of (2.3) it was shown in [5, eq. 9.31) that the negative real zero z n j ; j of Rn j ; j ( n j j )z) satisfies z n j ; j = z n j ; j O 1 (n j j ) 2 (j 1) 2.11) where z n j ; j denotes the real point of the arc D ....

de Bruin, M.G., Saff, E.B., Varga, R.S. (1981): On the zeros of generalized Bessel polynomials, I and II. Indag. Math. 43, 1--25

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC