Polyexponentials

Details Polyexponentials Polyexponentials

2007-10-05

arxiv.org/abs/0710.1332v1

Mathematics

Numerical Analysis

21 pages

Scientific paper

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.

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