Abstract
The main goal of this article is to study special polynomial power series expansions for entire axially monogenic functions. In relation to the difference and sum bases of monogenic polynomials, which have link with Bernoulli polynomials, the best possible bounds for the orders of such bases are determined. Moreover the T
ρ
-property of such differenced base and the sum base is discussed. The results obtained contain previous ones of complex setting as special cases.