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We investigate polynomial sets {P n } n$\ge$0 with generating power series ofthe form F (xt -- R(t)) and satisfying, for n $\ge$ 0, the (d + 1)-orderrecursion xP\_ n (x) = P\_{ n+1 }(x) +\sum\_{ l=0}^{d} \gamma^{l}\_{n} P\_{n--l} (x), where \ {\gamma ^{l}\_{ n}\ } is a complex sequence for 0 $\le$ l$\le$ d, P \_0 (x) = 1 and P \_n (x) = 0 for all negative integer n. We showthat the formal power series R(t) is a polynomial of degree at most d + 1 ifcertain coefficients of R(t) are null or if F (t) is a generalizedhypergeometric series. Moreover, for the d-symmetric case we demonstrate thatR(t) is the monomial of degree d + 1 and F (t) is expressed by hypergeometricseries.

On a Class of Polynomials Generated by F (xt -- R(t))