Taking the logarithm of binomial type sequences: linear approach

Abstract

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