Asymptotic Expansions for a Class of Orthogonal Polynomials on a Nite Interval
نویسنده
چکیده
An asymptotic expansion for the Jacobi polynomials and for the functions of the second kind is extended to the case of a weight function that is the product of the Jacobi weight function with an arbitrary positive analytic function.
منابع مشابه
Construction and implementation of asymptotic expansions for Laguerre-type orthogonal polynomials
Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval [0,∞) with respect to a weight function of the form w(x) = xαe−Q(x), Q(x) = m ∑ k=0 qkx , α > −1, qm > 0. The classical Laguerre polynomials correspond to Q(x) = x. The computation of higher-order terms of the asymptotic expansions of these polynomials for large degree becomes quite complicated, and a full descrip...
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