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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2000)
  6. Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$
 
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Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$

Ben Cheikh, Youssèf
2000
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ISSN
0049-4704
http://hdl.handle.net/10077/4259
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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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
Subjects
  • hypergeometric functi...

  • Brafman polynomials

  • Srivastava Panda plyn...

  • Decomposition with re...

Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
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.
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