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A note on the growth order of the inverse and product bases of special monogenic polynomials

The purpose of this paper is to generalize some theorems on the representation of certain classes of the entire special monogenic functions by inverse and product bases of special monogenic polynomials. We derive bounds for the order of inverse and product bases. Some examples are given showing that the resulting bounds are attainable. Our results improve and generalize some known results in Clifford setting concerning the order of inverse and product bases. Copyright © 2011 John Wiley & Sons, Ltd.