Taking the logarithm of binomial type sequences: linear approach

Abstract

In this paper we obtain the formal asymptotic expansion of the logarithms $\ln p_s(\hat{I}\pm )$ of $p_s(\hat{I}\pm )$, which are canonical continuations of polynomials of binomial type $p_n(\hat{I}\pm )$. Our approach is based on linear methods which do not require the calculation of expansions $(p_s(\hat{I}\pm )\hat{I}{\pm }^{-s}-1{)}^k$, as opposed to the direct logarithmization.

Typos corrected