Analytical and differential - algebraic properties of Gamma function

Simple item page
dc.creatorMijajlovic, Zarko
dc.creatorMalesevic, Branko
dc.date2006-05-16
dc.date2008-04-15
dc.date.accessioned2026-07-07T09:32:31Z
dc.date.available2026-07-07T09:32:31Z
dc.descriptionIn this paper we consider some analytical relations between gamma function $Γ(z)$ and related functions such as the Kurepa's function $K(z)$ and alternating Kurepa's function $A(z)$. It is well-known in the physics that the Casimir energy is defined by the principal part of the Riemann function $ζ(z)$ (Blau, Visser, Wipf; Elizalde). Analogously, we consider the principal parts for functions $Γ(z)$, $K(z)$, $A(z)$ and we also define and consider the principal part for arbitrary meromorphic functions. Next, in this paper we consider some differential-algebraic $($d.a.$)$ properties of functions $Γ(z)$, $ζ(z)$, $K(z)$, $A(z)$. As it is well-known (H\" older; Ostrowski) $Γ(z)$ is not a solution of any d.a. equation. It appears that this property of $Γ(z)$ is universal. Namely, a large class of solutions of functional differential equations also has that property. Proof of these facts is reduced, by the use of the theory of differential algebraic fields (Ritt; Kaplansky; Kolchin), to the d.a. transcendency of $Γ(z)$.
dc.descriptionPaper by invitation for The Special Volume dedicated to the Tricentennial Birthday Anniversary of L. Euler, 2007
dc.identifierhttps://arxiv.org/abs/math/0605430
dc.identifierhttp://arxiv.org/abs/math/0605430
dc.identifierInternational Journal of Applied Mathematics & Statistics, Vol.11, No. 7, November 2007, 118-129
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158808
dc.subjectGeneral Mathematics
dc.subjectComplex Variables
dc.subject03C60, 11R42, 11J91, 12H05, 30E20, 34M15
dc.titleAnalytical and differential - algebraic properties of Gamma function
dc.typetext

Files

Collections

arXiv