Asymptotic Expansions for Polynomials Orthogonal with Respect to a Complex Non-constant Weight Function
نویسندگان
چکیده
We consider a sequence of polynomials that are orthogonal with respect to a complex analytic weight function which depends on the index n of the polynomial. For such polynomials we obtain an asymptotic expansion in 1/n. As an example, we present the asymptotic expansion for Laguerre polynomials with a weight that depends on the index of the polynomial.
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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