Affiliation:
1. Department of Mathematics, Ohio Northern University, Ada 45810, Ohio, USA
Abstract
We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions forλ>0of the incomplete gamma functionγ(λ,x)and of the Lerch transcendentΦ(x,s,λ). In one particular case, our formula reduces to a series transformation formula which appears in the works of Ramanujan and is related to the exponential (or Bell) polynomials. Another particular case, based on the geometric series, gives rise to a new class of polynomials called geometric polynomials.
Subject
Mathematics (miscellaneous)
Cited by
41 articles.
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