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Uniform Asymptotic Expansions for Meixner Polynomials

✍ Scribed by X. -S. Jin; R. Wong

Publisher
Springer
Year
1997
Tongue
English
Weight
606 KB
Volume
14
Category
Article
ISSN
0176-4276

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The zeros of the Meixner polynomial m n (x; ;, c) are real, distinct, and lie in (0, ). Let : n, s denote the s th zero of m n (n:; ;, c), counted from the right; and let :Γ„ n, s denote the sth zero of m n (n:; ;, c), counted from the left. For each fixed s, asymptotic formulas are obtained for both

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It has been shown in Ferreira et al. [Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials, Adv. in Appl. Math. 31(1) (2003) 61-85], LΓ³pez and Temme [Approximations of orthogonal polynomials in terms of Hermite polynomials, Methods Appl. Anal. 6 (1999) 131-146; The Aske