Difference equations for a class of twice-iterated h-Appell sequences of polynomials

Abstract

In the present paper, we introduce a family of the twice-iterated h-Appell sequences of polynomials based upon the discrete Appell convolution of the h-Appell sequence of polynomials Qn(x). For these twice-iterated h-Appell polynomials, we prove an equivalence theorem and derive several determinantal properties in terms of the h-Appell polynomial sequence Qn(x). We also find the recurrence relation, the shift operators and the difference equation satisfied by the twice-iterated h-Appell polynomial sequences. By appropriately specializing our results, we obtain the corresponding properties for the sequences of the twice-iterated Bernoulli polynomials of the second kind, the twice-iterated Boole polynomials, the twice-iterated Boole-Bernoulli polynomials of the second kind, the twice-iterated Poisson-Charlier-Bernoulli polynomials of the second kind and the twice-iterated Poisson-Charlier-Boole polynomials.