𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A subadditive property of the gamma function

✍ Scribed by Horst Alzer; Stephan Ruscheweyh

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
116 KB
Volume
285
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Let βˆ† = min x 0 Ξ“ (2x)/Ξ“ (x) and Ξ± * = log 2/ log βˆ† = -0.946850. . . . We prove that the function x β†’ (Ξ“ (x)) Ξ± is subadditive on (0, ∞) if and only if Ξ± * Ξ± 0.

πŸ“œ SIMILAR VOLUMES

A submultiplicative property of the psi
A submultiplicative property of the psi function
✍ Horst Alzer; O.G. Ruehr πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 279 KB

We prove that the function x~--+ ~k(a+x) (a>0) is submultiplicative on [0, c~) if and only ifa~>a0 =3.203171 .... Here, a0 denotes the only positive real number which satisfies if(a0)= 1. (~) 1999 Elsevier Science B.V. All rights reserved.