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Annals of the Alexandru Ioan Cuza University - Mathematics

The Journal of "Alexandru Ioan Cuza" University from Iasi

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New Sharp Bounds for Gamma and Digamma Functions

Cristinel Mortici1

Department of Mathematics, Valahia University of Târgovişte, Bd. Unirii 18, 130082 Târgovişte, ROMANIA1

This content is open access.

Citation Information: Annals of the Alexandru Ioan Cuza University - Mathematics. Volume 57, Issue 1, Pages 57–60, ISSN (Print) 1221-8421, DOI: 10.2478/v10157-010-0037-1, February 2011

Publication History

Published Online:
2011-02-14

New Sharp Bounds for Gamma and Digamma Functions

Motivated by Sandor and Debnath, Batir, we prove that a function involving gamma function is completely monotonic. As applications, we establish new upper and lower bounds for the gamma and digamma functions, with sharp constants.

Keywords: factorial function; gamma function; digamma and polygamma functions; completely monotonic function; inequalities; Euler constant

  • Anderson, G. D.; Qiu, S.-L. - A monotoneity property of the gamma function, Proc. Amer. Math. Soc., 125 (1997), 3355-3362.

  • Andrews, G. E.; Askey, R.; Roy, R. - Special Functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, Cambridge, 1999.

  • Batir, N. - Sharp inequalities for factorial n, Proyecciones, 27 (2008), 97-102.

  • Guo, B.-N.; Qi, F. - An algebraic inequality, II, RGMIA Res. Rep. Coll., 4 (2001), 55-61.

  • Guo, S. - Monotonicity and concavity properties of some functions involving the gamma function with applications, JIPAM. J. Inequal. Pure Appl. Math., 7 (2006), Article 45, 7 pp.

  • Martins, J. S. - Arithmetic and geometric means, an applications to Lorentz sequence spaces, Math. Nachr., 139 (1988), 281-288.

  • Minc, H.; Sathre, L. - Some inequalities involving (r!)1/r, Proc. Edinburgh Math. Soc., 14 (1964/1965), 41-46.

  • Qi, F. - Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms Spec. Funct., 18 (2007), 503-509. [Web of Science]

  • Sandor, J.; Debnath, L. - On certain inequalities involving the constant e and their applications, J. Math. Anal. Appl., 249 (2000), 569-582.

  • Widder, D. V. - The Laplace Transform, Princeton Mathematical Series, Princeton University Press, Princeton, N. J., 1941.

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