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An algebraic structure for Faber polynomials
Authors:Gi-Sang Cheon  Hana Kim
Institution:a Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Rep. of Korea
b Department of Mathematics, Howard University, Washington, DC 20059, USA
Abstract:Let Σ be the set of functions, convergent for all |z|>1, with a Laurent series of the form f(z)=z+∑n?0anz-n. In this paper, we prove that the set of Faber polynomial sequences over Σ and the set of their normalized kth derivative sequences form groups which are isomorphic to the hitting time subgroup and the Bell(k) subgroup of the Riordan group, respectively. Further, a relationship between such Faber polynomial sequences and Lucas and Sheffer polynomial sequences is derived.
Keywords:Primary: 05A30  Secondary: 05A15
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