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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4259

Title: Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$
Authors: Ben Cheikh, Youssèf
Keywords: hypergeometric functions
Brafman polynomials
Srivastava Panda plynomials
Decomposition with respect to a cyclic group
Issue Date: 2000
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Youssèf Ben Cheikh, "Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2000), pp. 103-121.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
Abstract: Let $\left\{ P_{m}\right\} _{m\geq0}$ be a sequence of polynomials with complex coefficients and let n be an arbitrary positive integer. The components with respect to the cyclic group of order n of the polynomial $P_{m},m=0,1,...,$ are given by: \[ \left(P_{m}\right)_{\left[n,k\right]}\left(z\right)=\frac{1}{n}\overset{n-1}{\overset{\sum}{l=0}}\;\omega_{n}^{-kl}P_{m}\left(\omega_{n}^{l}z\right)\:,\quad k=0,1,...,n-1\;, \] where $\omega_{n}=exp\left(\frac{2i\pi}{n}\right)$. In this paper, we consider two class of hypergeometric polynomials, the Brafman polynomials and the Srivastava-Panda polynomials. For the components of these polynomials, we establish hypergeometric representations, differential equations and generating functions.
URI: http://hdl.handle.net/10077/4259
ISSN: 0049-4704
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.32 (2000)

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