The asymptotics of a second solution to the jacobi differential equation
Titel:
The asymptotics of a second solution to the jacobi differential equation
Auteur:
Wong, R. Zhang, J. -M.
Verschenen in:
Integral transforms and special functions
Paginering:
Jaargang 5 (1997) nr. 3-4 pagina's 287-308
Jaar:
1997-11
Inhoud:
An asymptotic expansion is derived for a second solution [image omitted] to the Jacobi differential equation, which is linearly independent of the Jacobi polynomial [image omitted] in the interval (-1,1). This expansion is valid uniformly with respect to x in the interval [image omitted] . A two-term asymptotic approximation is also constructed for the zeros [image omitted] , as n → ∞, where x = cosΘ. This approximation holds uniformly for k = 1,2,…,[γn], where γ can be any fixed number in (0,1).
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