Publicação: ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS
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Amer Mathematical Soc
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Acesso aberto
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.
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Jacobi polynomials, Laguerre polynomials, zeros, asymptotics
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Inglês
Como citar
Proceedings Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 144, n. 2, p. 535-545, 2016.
