Browsing by Subject "Completely monotonic functions"

Now showing items 1-8 of 8

    • Article  

      A Bernstein function related to Ramanujan's approximations of exp(n) 

      Koumandos, S. (2013)
      Ramanujan's sequence θ(n),n=0,1,2,..., is defined by en/2 =∑j=0 n-1nj/j!+nn/n! θ(n). It is possible to define, in a simple manner, the function θ(x) for all nonnegative real numbers x. We show that the function λ(x):=x ...
    • 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  

      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, ...
    • Article  

      On a conjecture for trigonometric sums and starlike functions, II 

      Koumandos, S.; Lamprecht, M. (2010)
      We prove the case ρ=1/4 of the following conjecture of Koumandos and Ruscheweyh: let snμ(z)=Σk=0n(μ)k/ k!zk, and for ρε(0,1] let μ≤(ρ) be the unique solution of 0(ρ+1)πsin(t-ρπ)tμ-1dt =0 in (0,1]. Then we have pipearg[(1 ...
    • 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  

      On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function 

      Koumandos, S. (2008)
      We study the remainder RN (x) in an asymptotic expansion due to S.N.M. Ruijsenaars, for the logarithm of the double gamma function. We show that for any even number N the function (- 1)frac(N, 2) - 1 RN (x) is completely ...
    • 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. ...