Abstract and Applied Analysis

Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives

Chun-Fu Wei and Bai-Ni Guo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Some complete monotonicity results that the functions ± 1 / e ± t - 1 are logarithmically completely monotonic, and that differences between consecutive derivatives of these two functions are completely monotonic, and that the ratios between consecutive derivatives of these two functions are decreasing on 0 ,   are discovered. As applications of these newly discovered results, some complete monotonicity results concerning the polylogarithm are found. Finally a conjecture on the complete monotonicity of the above-mentioned ratios is posed.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 851213, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276911

Digital Object Identifier
doi:10.1155/2014/851213

Mathematical Reviews number (MathSciNet)
MR3198263

Zentralblatt MATH identifier
07023195

Citation

Wei, Chun-Fu; Guo, Bai-Ni. Complete Monotonicity of Functions Connected with the Exponential Function and Derivatives. Abstr. Appl. Anal. 2014 (2014), Article ID 851213, 5 pages. doi:10.1155/2014/851213. https://projecteuclid.org/euclid.aaa/1412276911


Export citation

References

  • B.-N. Guo and F. Qi, “Some identities and an explicit formula for Bernoulli and Stirling numbers,” Journal of Computational and Applied Mathematics, vol. 255, pp. 568–579, 2014.
  • F. Qi, “Explicit formulas for computing Euler polynomials interms of the second kind Stirling numbers,” http://arxiv.org/ abs/1310.5921.
  • A.-M. Xu and Z.-D. Cen, “Some identities involving exponential functions and Stirling numbers and applications,” Journal of Computational and Applied Mathematics, vol. 260, pp. 201–207, 2014.
  • D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Classical and New Inequalities in Analysis, vol. 61, Kluwer Academic Publishers, 1993.
  • D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, USA, 1946.
  • R. L. Schilling, R. Song, and Z. Vondraček, Bernstein Functions, vol. 37 of de Gruyter Studies in Mathematics, De Gruyter, Berlin, Germany, 2010.
  • R. D. Atanassov and U. V. Tsoukrovski, “Some properties of a class of logarithmically completely monotonic functions,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 41, no. 2, pp. 21–23, 1988.
  • C. Berg, “Integral representation of some functions related to the gamma function,” Mediterranean Journal of Mathematics, vol. 1, no. 4, pp. 433–439, 2004.
  • F. Qi and Q. M. Luo, “Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezovic-Giordano-Pecaric's theorem,” Journal of Inequalities and Applications, vol. 2013, article 542, 20 pages, 2013.
  • F. Qi and Q.-M. Luo, “Bounds for the ratio of two gamma functions: from Wendel's and related inequalities to logarithmically completely monotonic functions,” Banach Journal of Mathe-matical Analysis, vol. 6, no. 2, pp. 132–158, 2012.
  • S. Koumandos and H. L. Pedersen, “On the asymptotic expansion of the logarithm of Barnes triple gamma function,” Mathematica Scandinavica, vol. 105, no. 2, pp. 287–306, 2009.
  • Wikipedia, “The Free Encyclopedia,” http://en.wikipedia.org/ wiki/Polylog.
  • F. Qi and B.-N. Guo, “Some logarithmically completely monotonic functions related to the gamma function,” Journal of the Korean Mathematical Society, vol. 47, no. 6, pp. 1283–1297, 2010.
  • S. Bochner, Harmonic Analysis and the Theory of Probability, California Monographs in Mathematical Sciences, University of California Press, Berkeley, Calif, USA, 1955. \endinput