In the setting of step two Carnot groups we give an explicit representation of Taylor polynomial in terms of a suitable basis of the real vector space of left invariant differential operators, acting pointwisely on monomials like the ordinary Euclidean iterated derivations.
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Gabriella Arena, Andrea O. Caruso, Antonio Causa, Taylor Formula on step two Carnot Groups. Rev. Mat. Iberoam. 26 (2010), no. 1, pp. 239–259DOI 10.4171/RMI/600