Physics – Mathematical Physics
Scientific paper
2011-01-22
Physics
Mathematical Physics
15 pages, no figures. Some new references. To appear in Publ. Math. Debrecen
Scientific paper
For $0\neq x>-1$ let $$\Delta(x)={{\ln \Gamma(x+1)} \over x}.$$ Recently Adell and Alzer proved the complete monotonicity of $\Delta'$ on $(-1,\infty)$ by giving an integral representation of $(-1)^n \Delta^{(n+1)}(x)$ in terms of the Hurwitz zeta function $\zeta(s,a)$. We reprove this integral representation in different ways, and then re-express it in terms of fractional part integrals. Special cases then have explicit evaluations. Other relations for $\Delta^{(n+1)}(x)$ are presented, including its leading asymptotic form as $x \to \infty$.
Coffey Mark W.
No associations
LandOfFree
Fractional part integral representation for derivatives of a function related to ln Gamma(x+1) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fractional part integral representation for derivatives of a function related to ln Gamma(x+1), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractional part integral representation for derivatives of a function related to ln Gamma(x+1) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-642368