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Decomposition of some hypergeometric polynomials with respect to the cyclic group of order $n$
Ben Cheikh, Youssèf
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
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.
Languages
en
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