Skip to main content
Log in

Some monotonicity properties and characterizations of the gamma function

  • Research Papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Anastassiadis, J.,Une propriété, de la fonction Gamma. Bull. Sci. Math. (2) 81 (1957), 116–118.

    MathSciNet  Google Scholar 

  2. Anastassiadis, J.,Définition des fonctions eulériennes par des équations fonctionelles. Mémorial des Sciences Mathématiques, fasc. 156., Gauthier-Villars, Paris, 1964.

    Google Scholar 

  3. Artin, E.,The gamma function. Athena series, Holt, Rinehart and Winston, New York, 1964; German original, B. G. Teubner, Leipzig, 1931.

    MATH  Google Scholar 

  4. Bohr, H. andMollerup, J.,Laerebog i matematisk Analyse, III. Jul. Gjellerups Forlag, Copenhagen, 1922.

    Google Scholar 

  5. Davis, P. J.,Leonhard Euler’s integral: a historical profile of the gamma function. Amer. Math. Monthly66 (1959), 849–869.

    Article  MATH  MathSciNet  Google Scholar 

  6. Erdélyi, A., et al.,Higher transcendental functions, vol. 1. McGraw-Hill, New York, 1953.

    Google Scholar 

  7. Feller, W.,Completely monotone functions and sequences. Duke Math. J. 5 (1939), 661–674.

    Article  MathSciNet  Google Scholar 

  8. John, F.,Special solutions of certain difference equations. Acta Math. 71 (1939), 175–189.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kairies, H.-H.,Zur axiomatischen Characterisierung der Gammafunktion. J. Reine Angew. Math. 236 (1969), 103–111.

    MATH  MathSciNet  Google Scholar 

  10. [10]Kairies, H.-H.,Über die logarithmische Ableitung der Gammafunktion. Math. Ann. 184 (1970), 157–162.

    Article  MATH  MathSciNet  Google Scholar 

  11. Kimberling, C. H.,Two-dimensional complete monotonicity with diagonalization. Amer. Math. Monthly 80 (1973), 789–791.

    Article  MATH  MathSciNet  Google Scholar 

  12. Krull, W.,Bemerkungen zur Differenzenglcichung g(χ + 1)- g(χ) = ϕ(χ). Math. Nachr. I (1948), 365–376.

    Article  MathSciNet  Google Scholar 

  13. Krull, W.,Bemerkungen zur Differenzengleichung g(χ+l)-g(χ)=ϕ(χ), II. Math. Nachr. 2 (1949), 251–262.

    Article  MATH  MathSciNet  Google Scholar 

  14. Kuczma, M.,Functional equations in a single variable. Monografie Matematyczne, Tom 46, Pafistwowe Wydawnictwo Naukowe, Warsaw, 1968.

    Google Scholar 

  15. [15]Lazarevic, I. B., andLupas, A.,Functional equations for Wallis and gamma functions. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 461-497, 245–251 (1974).

    Google Scholar 

  16. Mayer, A. E.,Konvexe Lösung der Funktionalgleichung 1/f(χ+ 1)=χf(χ). Acta Math. 70 (1939), 57–62.

    Article  MathSciNet  Google Scholar 

  17. Muldoon, M. E.,Some characterizations of the gamma function involving the notion of complete monotonicity. Aequationes Math. 8 (1972), 212–215.

    Article  MathSciNet  Google Scholar 

  18. Oldham, K. I. andSpanier, J.,The fractional calculus. Academic Press, New York and London, 1974.

    MATH  Google Scholar 

  19. Widder, D. V.,The Laplace transform. Princeton University Press, Princeton, N.J., 1941.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported by grants from the Canada Council and the National Research Council.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muldoon, M.E. Some monotonicity properties and characterizations of the gamma function. Aeq. Math. 18, 54–63 (1978). https://doi.org/10.1007/BF01844067

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01844067

Keywords

Navigation