The q-Sheffer sequences of a new type and associated orthogonal polynomials

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• 作者：Gi-Sang Cheon¹ ; ^{gscheon@skku.edu" class="auth_mail" title="E-mail the corresponding author} ; Ji-Hwan Jung ^{jh56k@skku.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 05A15 ; secondary ; 12D10
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：491
• 期：Complete
• 页码：171-186
• 全文大小：479 K

文摘

Using q-Riordan matrices in terms of the Eulerian generating functions we formulate the q-Sheffer sequences of a new type. This concept may differ from others in the literature appeared previously. We also give some conditions for q-Sheffer sequences to be orthogonal. As an application, we obtain the Eulerian generating functions for orthogonal polynomials of some special types. In addition, we consider interlacing properties for the zeros, particularly complex zeros of the orthogonal q-Sheffer sequence extending both the Hermite polynomials and the Chebyshev polynomials of the second kind.