Polyexponentials
Numerical Analysis
2007-10-09 v1 Classical Analysis and ODEs
Abstract
We discuss a special function (polyexponential) that extends the natural exponential function and also the exponential integral. The basic properties of the polyexponential are listed and some applications are given. In particular, it is shown that certain Mellin integrals can be evaluated in terms of polyexponentials. The polyexponential is related to the exponential polynomials, the Riemann zeta function, the Dirichlet eta function and the Lerch Transcendent.
Keywords
Cite
@article{arxiv.0710.1332,
title = {Polyexponentials},
author = {Khristo N. Boyadzhiev},
journal= {arXiv preprint arXiv:0710.1332},
year = {2007}
}
Comments
21 pages