Artículos de revistas
Zeros of Jacobi functions of second kind
Fecha
2006-04-01Registro en:
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 188, n. 1, p. 65-76, 2006.
0377-0427
10.1016/j.cam.2005.03.055
WOS:000234789100005
WOS000234789100005.pdf
1681267716971253
Autor
Univ Vigo
Universidade Estadual Paulista (Unesp)
Univ Catholique Louvain
Institución
Resumen
The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.