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Abstract: We discuss a special function polyexponential that extends the naturalexponential function and also the exponential integral. The basic properties ofthe polyexponential are listed and some applications are given. In particular,it is shown that certain Mellin integrals can be evaluated in terms ofpolyexponentials. The polyexponential is related to the exponentialpolynomials, the Riemann zeta function, the Dirichlet eta function and theLerch Transcendent.

Author: Khristo N. Boyadzhiev

Source: https://arxiv.org/

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