A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Anshelevich, Michael
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 4(2016)
• Page Start: 307
• Page End: 317
• Publication Date: 2016-04-02
• Subjects: Orthogonal polynomials -- generating functions -- Boas–Buck polynomials -- ultrasphericalpolynomials -- Chebyshev polynomials; Primary: 33C45 -- Secondary: 42C05 -- 46L54; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2015.1121385
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We show that the only orthogonal polynomials with a generating function of the form F ( x z − α z 2 ) are the ultraspherical, Hermite, and Chebyshev polynomials of the first kind. For special F for which this is the case, we then finish the classification of orthogonal polynomials with more general generating functions F ( x w ( z ) − R ( z ) ) .