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A factorization formula for power series

Abstract : Given an odd prime p, we give an explicit factorization over the ring of formal power series with integer coefficients for certain reducible polynomials whose constant term is of the form $p^w$ with $w>1$. Our formulas are given in terms of partial Bell polynomials and rely on the inversion formula of Lagrange.
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Daniel Birmajer, Juan B. Gil, Michael D. Weiner. A factorization formula for power series. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.935-944. ⟨hal-01207562⟩

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