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

2016/05/17 by Mohammed Mesk, Mesk, Mohammed, Mohammed Brahim Zahaf +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1605.05181

openalex publication_date 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the only polynomial sets with a generating function of the form F (xt -- R(t)) and satisfying a three-term recursion relation are the monomial set and the rescaled ultraspherical, Hermite, and Chebyshev polynomials of the first kind.

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