An operator on formal power series of the form SμS , where μ is an invertible power series, and σ is a series of the form t+（t2） is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ，σ ） , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .
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G. H. E. Duchamp, L. Poinsot, A. I. Solomon, K. A. Penson, P. Blasiak and A. Horzela, “Ladder Operators and Endomorphisms in Combinatorial Physics,” Discrete Mathematics and Theoretical Computer Science, Vol. 12, No. 2, 2010, pp. 23-46.