Ratio and Plancherel-Rotach asymptotics for Meixner-Sobolev orthogonal polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:116

Article

Area, I ; Godoy, E ; Marcellán, F ; Moreno-Balcázar, JJ

关键词: Sobolev orthogonal polynomials;    Meixner polynomials;    scaled polynomials;    asymptotics;    Plancherel-Rotach asymptotics;   

DOI  :  10.1016/S0377-0427(99)00281-2

来源: Elsevier

【 摘 要 】

We study the analytic properties of the monic Meixner-Sobolev polynomials {Q(n)} orthogonal with respect to the inner product involving differences [GRAPHICS] where lambda greater than or equal to 0, Delta is the forward difference operator (Delta f(x) = f(x + 1) - f(x)) and (gamma)(n) denotes the Pochhammer symbol. Relative asymptotics for Meixner-Sobolev polynomials with respect to Meixner polynomials is obtained. This relative asymptotics is also given for the scaled polynomials. Moreover, a zero distribution for the scaled Meixner-Sobolev polynomials and Plancherel-Rotach asymptotics for {Q(n)} are deduced. (C) 2000 Elsevier Science B.V. All rights reserved.

【 授权许可】

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