Decomposition of some hypergeometric polynomials with respect to the cyclic group of order \(n\) (Q2764716)

Let \(\{P_m\}^\infty_{m=0}\) 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 \(P_m (m=0,1,2, \dots)\), are given by NEWLINE\[NEWLINE(P_m)_{[n,k]} (z)={1\over n}\sum^{n-1}_{l=0} \omega_n^{-kl} P_m(\omega^l_nz) \quad(k=0,1, \dots,n-1),NEWLINE\]NEWLINE where \(\omega_n= \exp ({2p\pi \over n})\). In this paper the author considers two classes of hypergeometric polynomials, the Brafman polynomials and the Srivastava-Panda polynomials (see the reviewer and \textit{R. Panda} [Boll. Unione Mat. Ital., V. Ser., A 16, 467-474 (1979; Zbl 0406.33009)]). For the components of these polynomials, he establishes hypergeometric representations, differential equations, and generating functions.