Browsing by Subject "Gamma function"

Now showing items 1-7 of 7

    • Article  

      Complete monotonicity and related properties of some special functions 

      Koumandos, S.; Lamprecht, M. (2013)
      We completely determine the set of s, t > 0 for which the function is a Bernstein function, that is Ls,t(x) is positive with completely monotonic derivative on (0, ∞). The complete monotonicity of several closely related ...
    • Article  

      Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function 

      Koumandos, S.; Pedersen, H. L. (2009)
      We introduce completely monotonic functions of order r > 0 and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic ...
    • Article  

      Monotonicity of some functions involving the gamma and PSI functions 

      Koumandos, S. (2008)
      Let L(x): = x - Γ(x+t)/Γ(x+s) xs-t+1, where Γ(x) is Euler's gamma function. We determine conditions for the numbers s, t so that the function Ψ(x): = - Γ(x-s)/Γ(x+t) x t-s-1 L″(x) is strongly completely monotonie on (0, ...
    • Book Chapter  

      On completely monotonic and related functions 

      Koumandos, S. (Springer New York, 2014)
      We deal with several classes of functions, such as, completely monotonic functions, absolutely monotonic functions, logarithmically completely monotonic functions, Stieltjes functions, and Bernstein functions. We give ...
    • Article  

      Remarks on a paper by Chao-Ping Chen and Feng Qi 

      Koumandos, S. (2006)
      In a recent paper, Chao-Ping Chen and Feng Qi (2005) established sharp upper and lower bounds for the sequence Pn := 1.3...(2n-1)/2.4...2n. We show that their result follows easily from a theorem of G. N Watson published ...
    • Article  

      Remarks on some completely monotonic functions 

      Koumandos, S. (2006)
      Applying the Euler-Maclaurin summation formula, we obtain upper and lower polynomial bounds for the function frac(x, ex - 1), x > 0, with coefficients the Bernoulli numbers Bk. This enables us to give simpler proofs of ...
    • Article  

      Some completely monotonic functions of positive order 

      Koumandos, S.; Lamprecht, M. (2010)
      We completely determine the set of (α, β) ∈ ℝ2for which the function is convex on (0, ∞) and use this result to give some special classes of completely monotonic functions of positive order related to gamma and psi functions. ...