Zeros of Jacobi functions of second kind
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Data
2006-04-01
Autores
Area, I
Dimitrov, D. K.
Godoy, E.
Ronveaux, A.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
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.
Descrição
Palavras-chave
Jacobi functions of second kind, zeros, Jacobi polynomials, interlacing properties of zeros, Laguerre and Hermite functions of second kind
Como citar
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 188, n. 1, p. 65-76, 2006.