A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind

作者：Anshelevich Michael^*

来源：Integral Transforms and Special Functions, 2016, 27(4): 307-317.

DOI：10.1080/10652469.2015.1121385

• 46L54
• Primary: 33C45
• Secondary: 42C05
• generating functions
• Boas-Buck polynomials
• Chebyshev polynomials
• Orthogonal polynomials
• ultrasphericalpolynomials

We show that the only orthogonal polynomials with a generating function of the form
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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
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.

• 出版日期2016-4-2