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|Title:||Asymptotic behaviour of Jacobi polynomials and their zeros|
|Author:||Dimitrov, Dimitar K.|
dos Santos, Eliel J. C.
|Abstract:||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|
|Subject:||Polinômios de Jacobi|
|Editor:||American Mathematical Society|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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