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

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• 作者：Mohammed Mesk^a ; ^{m_mesk@yahoo.fr} ; Mohammed Brahim Zahaf^b ; ^c ; ^{m_b_zahaf@yahoo.fr}
• 关键词：Orthogonal polynomials ; Generating functions ; Recurrence relations ; Ultraspherical polynomials ; Chebyshev polynomials ; Hermite polynomials
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1147-1162
• 全文大小：376 K
• 卷排序：448

文摘

We show that the only polynomial sets with a generating function of the form F(xt−R(t))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.