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.

Keywords

• partial bell polynomials
• factorization of formal power series
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]