English

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

R2 v1 2026-06-21T09:27:41.843Z