Some properties of the gamma and PSI functions, with applications

: Qiu S., Vuorinen M.

: 2005

: Mathematics of Computation

: 74

: 250

: 723

: 742

: 0025-5718

DOI: https://doi.org/10.1090/S0025-5718-04-01675-8

: http://api.elsevier.com/content/abstract/scopus_id:14944340570

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 Ω of the unit ball B ⊂ ℝ , the surface area ω of the unit sphere S , and some related constants. © 2004 American Mathematical Society.