Browsing by Author "Koumandos, S."
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Article
Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function
Koumandos, S.; Pedersen, H. L. (2011)It is shown that the remainders in asymptotic expansions of the logarithm of Barnes double and triple gamma function and Euler's gamma function are Laplace transformations of positive multiples of absolutely monotonic ...

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 n1nj/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
Companions of the inequalities of FejérJackson and young
Alzer, H.; Koumandos, S. (2005)Applications of some wellknown theorems of Jackson and Young lead to the sharp inequalities, We prove that the following counterpart is valid for all integers n ≥ 1 and real numbers x ∈ (0, π): where the sign of equality ...

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
Continuous singular measures with absolutely continuous convolution squares on locally compact groups
Karanikas, C.; Koumandos, S. (1991)

Article
An extension of Vietoris's inequalities
Koumandos, S. (2007)We establish a best possible extension of a famous Theorem of Vietoris about the positivity of a general class of cosine sums. Our result refines and sharpens several earlier generalizations of this Theorem, and settles ...

Article
Inequalities for trigonometric sums
Koumandos, S. (2012)We give a survey of recent results on positive trigonometric sums. Farreaching extensions and generalizations of classical results are presented. We provide new proofs as well as additional remarks and comments. We also ...

Article
Inequalities for two sine polynomials
Alzer, H.; Koumandos, S. (2006)We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0, π) we have (Formula Presented) with the best possible constant bounds (Formula Presented) (II) The inequality (Formula Presented) holds for all even integers n ...

Article
Inequalities of FejérJackson Type
Alzer, H.; Koumandos, S. (2003)We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical FejérJackson inequality: For all integers n ≥ 2 and real numbers x ∈ (0, π) we have ...

Article
L”Convergence of a Certain Class of Product Martingales
Koumandos, S. (1994)We establish the Kakutani dichotomy property for two generalized RademacherRiesz product measures p, v

Article
Monotonic trigonometric sums and coefficients of bloch functions
Koumandos, S. (1999)We establish a new class of monotonic trigonometric sums. Through a result of Andreev and Duren, our theorem provides information about the coefficients of certain Bloch functions.

Article
Monotonicity of some functions involving the gamma and PSI functions
Koumandos, S. (2008)Let L(x): = x  Γ(x+t)/Γ(x+s) xst+1, where Γ(x) is Euler's gamma function. We determine conditions for the numbers s, t so that the function Ψ(x): =  Γ(xs)/Γ(x+t) x ts1 L″(x) is strongly completely monotonie on (0, ...

Article
A new bound for the FejérJackson sum
Brown, G.; Koumandos, S. (1998)We establish a new positive functional estimate for the FejérJackson sum Sn(θ) = Σnk=1 k1 sin kθ. This result enables us to give a simple proof of a result of Askey and Steinig on a monotonic sine sum associated with the ...

Article
A new refinement of Young's inequality
Alzer, H.; Koumandos, S. (2007)A classical theorem due to Young states that the cosine polynomial c n(x) = 1 + ∑k=1n cos(kx)/k is positive for all n ≥ 1 and x ∈ (0, π). We prove the following refinement. For all n ≥ 2 and x ∈ [0, π] we have 1/6 + c(π  ...

Article
On a class of integrals involving a Bessel function times gegenbauer polynomials
Koumandos, S. (2007)We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and ...

Article
On a conjecture for trigonometric sums and starlike functions
Koumandos, S.; Ruscheweyh, S. (2007)We pose and discuss the following conjecture: let snμ (z) {colon equals} ∑k = 0n frac((μ)k, k !) zk, and for ρ ∈ (0, 1] let μ* (ρ) be the unique solution μ ∈ (0, 1] of ∫0(ρ + 1) π sin fenced(t  ρ π) tμ  1 dt = 0 .Then ...

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(tρπ)tμ1dt =0 in (0,1]. Then we have pipearg[(1 ...

Article
On a conjecture of Clark and Ismail
Alzer, H.; Berg, C.; Koumandos, S. (2005)Let Φm (x) = xmψ(m) (x), where ψ denotes the logarithmic derivative of Euler's gamma function. Clark and Ismail prove in a recently published article that if m ∈ {1,2,..., 16}, then Φm(m) is completely monotonic on (0, ...

Article
On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials
Koumandos, S. (2007)Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality (equation presented) holds for α, β >  1 and n ≥ 1, θ∈ ∈(0, π), where Pn(α,β)(x) are the ...