Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On some properties of the Gamma function

Authors: Árpád Elbert and Andrea Laforgia
Journal: Proc. Amer. Math. Soc. 128 (2000), 2667-2673
MSC (2000): Primary 33B15; Secondary 26A48, 26D07
Published electronically: March 1, 2000
MathSciNet review: 1694859
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Anderson and Qiu (1997) conjectured that the function $\frac{\log \Gamma (x+1)}{{x \log x}}$is concave for $x>1$. In this paper we prove this conjecture. We also study the monotonicity of some functions connected with the psi-function $\psi (x)$ and derive inequalities for $\psi (x)$ and $\psi '(x)$.

References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965. MR 31:1400
  • [2] H. Alzer, On some inequalities for the gamma and psi functions, Math. Comp. 66 (1997), 373-389. MR 97e:33004
  • [3] G. D. Anderson and S.-L. Qiu, A monotoneity property of the gamma function, Proc. Amer. Math. Soc. 125 (1997), 3355-3362. MR 98h:33001
  • [4] B. C. Carlson, Special Functions of Applied Mathematics, Academic Press, New York, 1977. MR 58:28707
  • [5] M. E. Muldoon, Some monotonicity properties and characterizations of the gamma function, Aequationes Math. 18 (1978), 54-63. MR 58:11536

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 33B15, 26A48, 26D07

Retrieve articles in all journals with MSC (2000): 33B15, 26A48, 26D07

Additional Information

Árpád Elbert
Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, Budapest H-1364, Hungary

Andrea Laforgia
Affiliation: Department of Mathematics, Largo S. Leonardo Murialdo, 1 00146 Roma, Italy

Keywords: Gamma function, psi function, monotonicity, inequalities
Received by editor(s): October 23, 1998
Published electronically: March 1, 2000
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society