A general method for deriving some semi-classical properties of perturbed second degree forms: The case of the Chebyshev form of second kind

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摘要

We present a new general method and the corresponding symbolic algorithm PSDF for deriving some semi-classical properties of perturbed second degree forms namely: the Stieltjes function, the Stieltjes equation, the functional equation, the class, a structure relation and the second order linear differential equation. We give new explicit results for some perturbed of order 3 of the second kind Chebyshev polynomials.

论文关键词:34,33C45,33D45,42C05,33F10,68W30,62-09,33F05,65D20,68-04,Orthogonal polynomials,Perturbed forms,Semi-classical forms,Second-degree forms,Chebyshev form of second kind

论文评审过程:Received 23 March 2015, Revised 21 September 2015, Available online 29 October 2015, Version of Record 12 November 2015.

论文官网地址:https://doi.org/10.1016/j.cam.2015.10.016