Some considerations in connection with Kurepa's function

2004/06/11 by Branko J. Malesevic
Mathematics · Physics and Astronomy · #math.NT #math-ph #math.CV #math.MP #msc:30E20 #msc:11J91

paper · pdf

published as Univ. Beograd. Publ. Elektrotehn. Fak., Ser. Mat. 14 (2003), 30-40 · 11 pages

arxiv created 2004/06/11 · arxiv updated 2009/12/01

Abstract

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function K(z) \citeKurepa₇1 and function K₁(z)). We determine an extension of domain of functions K(z) and K₁(z) in the sense of Cauchy's principal value at point \citeSlavic₇0. In this paper we give an addendum to the proof of Slavi' c's representation of Kurepa's function K(z) \citeSlavic₇3. Also, we consider some representations of functions K(z) and K₁(z) via incomplete gamma function and we consider differential transcendency of previous functions too.

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