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Logarithmically completely monotonic functions relating to the gamma function
 J. Math. Anal. Appl
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Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, submitted
"... Abstract. In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel’s, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, LazarevićLupa¸s’s, Kershaw’s and ElezovićGiordanoPečarić’s inequalities, clai ..."
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Cited by 7 (5 self)
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Abstract. In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel’s, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, LazarevićLupa¸s’s, Kershaw’s and ElezovićGiordanoPečarić’s inequalities, claim, monotonic and convex properties. On the other hand, we introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years. Contents
NECESSARY AND SUFFICIENT CONDITIONS FOR A FUNCTION INVOLVING DIVIDED DIFFERENCES OF THE DI AND TRIGAMMA FUNCTIONS TO BE COMPLETELY MONOTONIC
, 903
"... Abstract. In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two g ..."
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Abstract. In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bounding divided differences of polygamma functions. 1.
A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a powerexponential function, submitted
 CLASS OF COMPLETELY MONOTONIC FUNCTIONS AND APPLICATIONS 11
"... Abstract. In the article, a notion “logarithmically absolutely monotonic function” is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the ..."
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Abstract. In the article, a notion “logarithmically absolutely monotonic function” is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function α x+β 1+ are proved, where α and β are given real parameters, a new proof x for the inclusion that a logarithmically completely monotonic function is also completely monotonic is given, and an open problem is posed.
Complete monotonicity of some functions involving polygamma functions, submitted
"... Abstract. In the present paper, we establish necessary and sufficient conditions for the functions x α ˛ ˛ψ (i) (x + β) ˛ ˛ and α ˛ ˛ψ (i) (x + β) ˛ ˛ − x ˛ ˛ψ (i+1) (x + β) ˛ ˛ respectively to be monotonic and completely monotonic on (0, ∞), where i ∈ N, α> 0 and β ≥ 0 are scalars, and ψ ( ..."
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Abstract. In the present paper, we establish necessary and sufficient conditions for the functions x α ˛ ˛ψ (i) (x + β) ˛ ˛ and α ˛ ˛ψ (i) (x + β) ˛ ˛ − x ˛ ˛ψ (i+1) (x + β) ˛ ˛ respectively to be monotonic and completely monotonic on (0, ∞), where i ∈ N, α> 0 and β ≥ 0 are scalars, and ψ (i) (x) are polygamma functions. 1.
LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING p − GAMMA FUNCTIONS
"... Abstract. In this paper we prove that the function fα,β,p(x) = Γp(x + β) px (x + xx+β−α () 2, and ..."
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Abstract. In this paper we prove that the function fα,β,p(x) = Γp(x + β) px (x + xx+β−α () 2, and
Monotonicity and logarithmic convexity relating to the volume of the unit ball, submitted
"... Abstract. Let Ωn stand for the volume of the unit ball in Rn for n ∈ N. In the 1/(n ln n) present paper, we prove that the sequence Ωn is logarithmically convex 1/(n ln n) Ω and that the sequence is strictly decreasing for n ≥ 2. In n Ω 1/[(n+1)ln(n+1)] n+1 addition, some monotonic and concave prope ..."
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Abstract. Let Ωn stand for the volume of the unit ball in Rn for n ∈ N. In the 1/(n ln n) present paper, we prove that the sequence Ωn is logarithmically convex 1/(n ln n) Ω and that the sequence is strictly decreasing for n ≥ 2. In n Ω 1/[(n+1)ln(n+1)] n+1 addition, some monotonic and concave properties of several functions relating to Ωn are extended and generalized.
Asian options and meromorphic Lévy processes
"... One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. ..."
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Cited by 1 (1 self)
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One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy process. We prove that the exponential functional is equal in distribution to an infinite product of indepedent beta random variables, and its Mellin transform can be expressed as an infinite product of gamma functions. We show that these results lead to an efficient algorithm for computing the price of the Asian option via the inverse MellinLaplace transform, and we compare this method with some other techniques.
Full Screen
, 2007
"... Abstract: This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered. ..."
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Abstract: This note gives a simple method for obtaining inequalities for ratios involving 3logconvex functions. As an example, an inequality for Wallis’s ratio of GautchiKershaw type is obtained. Inequalities for generalized means are also considered.
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, 2006
"... A class of logarithmically completely monotonic functions related to (1 + 1/x)x and an application 1 ..."
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A class of logarithmically completely monotonic functions related to (1 + 1/x)x and an application 1