Volume 3,  Issue 5, 2002

Article 73

A MONOTONICITY PROPERTY OF THE G FUNCTION

HENDRIK VOGT AND JÜRGEN VOIGT

FACHRICHTUNG MATHEMATIK, 
TECHNISCHE UNIVERSITÄT DRESDEN, 
D-01062 DRESDEN, GERMANY
E-Mail: vogt@math.tu-dresden.de

E-Mail: voigt@math.tu-dresden.de

 

Received 11 January, 2001; Accepted 29 July, 2002.
Communicated by: A. Laforgia


ABSTRACT.    It is shown that the function $x \mapsto 1+\frac1x\ln\Gamma(x+1)-\ln(x+1)$ is strictly completely monotone on $(-1,\infty)$ and tends to one as $x\to-1$, to zero as $x\to\infty$. This property is derived from a suitable integral representation of $\ln\Gamma(x+1)$.
Key words:
Gamma function, Strictly completely monotone.

2000 Mathematics Subject Classification:
33B15.


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