The complete Bell polynomials for certain arguments in terms of Stirling numbers of the first kind

AbstractThe value of the (exponential) complete Bell polynomials for certain arguments, given essentially by finite sums of reciprocal powers with a real parameter, is expressed in terms of coefficients generated by the power series expansion of a Pochhammer symbol. This result generalizes an earlier result given by Comtet, which relates these polynomials for certain arguments to Stirling numbers of the first kind