Abstract
Asymptotic properties of orthogonal Laurent (L-) polynomialsV n (z), associated with log-normal distributions, are derived by constructive methods. It is shown that the sequences {V 2n (z)} and {V 2n+1 (z)} converge separately (asn→∞) to functionsV (0) (z) andV (1) (z), respectively, both holomorphic in 0<|z|<∞. Explicit Laurent series expansions are obtained, from which it follows that each limit function has essential, isolated singularities atz=0 andz=∞.
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Communicated by Tom H. Koornwinder.
Dedicated to R. S. Varga on the occasion of his 60th birthday.
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Cooper, S.C., Jones, W.B. & Thron, W.J. Asymptotics of orthogonal L-polynomials for log-normal distributions. Constr. Approx 8, 59–67 (1992). https://doi.org/10.1007/BF01208906
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DOI: https://doi.org/10.1007/BF01208906