AbstractIn the spirit of our earlier paper  and Zhang and Wang ,we introduce the matrix of multiplicative q-Appell polynomials of order M ∈ ℤ. This is the representation of the respective q-Appell polynomials in ke-ke basis. Based on the fact that the q-Appell polynomials form a commutative ring , we prove that this set constitutes a q-Lie group with two dual q-multiplications in the sense of . A comparison with earlier results on q-Pascal matrices gives factorizations according to , which are specialized to q-Bernoulli and q-Euler polynomials.We also show that the corresponding q-Bernoulli and q-Euler matrices form q-Lie subgroups. In the limit q → 1 we obtain corresponding formulas for Appell polynomial matrices.We conclude by presenting the commutative ring of generalized q-Pascal functional matrices,which operates on all functions f ∈ C∞q .
Special Matrices – de Gruyter
Published: Mar 2, 2018
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