ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS

Autor(es)

Dimitrov, Dimitar K. ^[1] ; dos Santos, Eliel J. C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 144, n. 2, p. 535-545, FEB 2016.
• Citações Web of Science: 1

Resumo

We obtain the explicit form of the expansion of the Jacobi polynomial P-n((alpha, beta)) (1 - 2x/beta) in terms of the negative powers of beta. It is known that the constant term in the expansion coincides with the Laguerre polynomial L-n((alpha))(x). Therefore, the result in the present paper provides the higher terms of the asymptotic expansion as beta -> infinity. The corresponding asymptotic relation between the zeros of Jacobi and Laguerre polynomials is also derived. (AU)

• Processo FAPESP: 09/13832-9 - Polinômios ortogonais, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático