## SOME PROPERTIES OF THE GAMMA AND PSI FUNCTIONS, WITH APPLICATIONS

by
S. -l. Qiu
,
M. Vuorinen

Citations: | 5 - 0 self |

### BibTeX

@MISC{Qiu_someproperties,

author = {S. -l. Qiu and M. Vuorinen},

title = {SOME PROPERTIES OF THE GAMMA AND PSI FUNCTIONS, WITH APPLICATIONS},

year = {}

}

### OpenURL

### Abstract

Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some well-known results for the volume Ωn of the unit ball B n ⊂ R n,thesurface area ωn−1 of the unit sphere S n−1, and some related constants. 1.