Asymptotic expansions of a class of hypergeometric polynomials with respect to the order
β Scribed by Jerry L Fields; Yudell L Luke
- Publisher
- Elsevier Science
- Year
- 1963
- Tongue
- English
- Weight
- 407 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx = e -Q(x) dx on the real line, where Q(x) = β 2m k=0 q k x k , q 2m > 0, denotes a polynomial of even order with positive leading coefficient. The orthogonal polynomial problem is formulated as a Riemann-Hilbert problem
Given a polynomial solution of a differential equation, its m-ary decomposition, i.e. its decomposition as a sum of m polynomials P [j] (x) = k Ξ± j,k x Ξ» j,k containing only exponents Ξ» j,k with Ξ» j,k+1 -Ξ» j,k = m, is considered. A general algorithm is proposed in order to build holonomic equations