Series expansions related to the logarithmic mean

József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 54—57
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Authors and affiliations

József Sándor
Babeș-Bolyai University, Department of Mathematics
Cluj, Romania

Abstract

We show that the Gregory series combined with Newton’s binomial expansion give a natural approach to the logarithmic mean inequalities.

Keywords

  • Gregory series
  • Newton binomial series
  • Logarithmic mean

AMS Classification

  • 26D15
  • 26D99
  • 26A06

References

  1. Alzer, H. (1986) Ungleichungen fur Mittelwerte, Arch. Math. (Basel), 47, 422–426.
  2. Carlson, B. C. (1972) The logarithmic mean, Amer. Math. Monthly, 79, 615–618. 56
  3. Hairer, E., & Wanner, G. (2008) Analysis by its history, Springer Verlag.
  4. Leach, E. B., & Sholander, M. C. (1983) Extended mean values II, J. Math. Anal. Appl., 92, 207–223.
  5. Lin, T. P. (1974) The power mean and the logarithmic mean, Amer. Math. Monthly, 81, 879–883.
  6. Sándor, J. (1988) Some integral inequalities, Elem. Math., 43, 177–180.
  7. Sándor, J. (1990) On the identric and logarithmic means, Aequationes Math., 40, 261–270.
  8. Sándor, J. (1991) A note on some inequalities for means, Arch. Math. (Basel), 56, 471–473.
  9. Sándor, J. (1995) On certain inequalities for means, J. Math. Anal. Appl., 189, 402–606.
  10. Sándor, J. (2008) Some simple integral inequalities, Octogon Math. Mag., 16(2), 925–933.
  11. Sándor, J. (2012) On a logarithmic inequality, Bull. Intern. Math. Virtual Inst., 2, 219–221.
  12. Sándor, J. (2013) New refinements of two inequalities for means, J. Math. Ineq., 7(2), 251– 254.
  13. Sándor, J. (2014) Buniakowsky and the logarithmic mean inequalities, RGMIA Research Report Collection, 17(5), 1–5.
  14. Sándor, J. (2015) A basic logarithmic inequality and the logarithmic mean, Notes Number Th. Discr. Math., 21(1), 31–35.
  15. Sándor, J. (2016) A note on the logarithmic mean, Amer. Math. Monthly, 123(1), 112.
  16. Stolarsky, K. B. (1980) The power and generalized logarithmic means, Amer. Math. Monthly, 87, 545–548. 57.

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Cite this paper

APA

Sándor, J. (2016). Series expansions related to the logarithmic mean. Notes on Number Theory and Discrete Mathematics, 22(2), 54-57.

Chicago

Sándor, József. “Series Expansions Related to the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 54-57.

MLA

Sándor, József. “Series Expansions Related to the Logarithmic Mean.” Notes on Number Theory and Discrete Mathematics 22.2 (2016): 54-57. Print.

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