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38
A COMPLETELY MONOTONIC FUNCTION INVOLVING THE GAMMA AND TRIGAMMA FUNCTIONS
, 2013
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NECESSARY AND SUFFICIENT CONDITIONS FOR A FUNCTION INVOLVING DIVIDED DIFFERENCES OF THE DI AND TRIGAMMA FUNCTIONS TO BE COMPLETELY MONOTONIC
, 2009
"... 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 func ..."
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Cited by 18 (15 self)
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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.
Complete monotonicity of some functions involving polygamma functions
, 2009
"... 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) ar ..."
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Cited by 13 (10 self)
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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.
Sharp inequalities for the psi function and harmonic numbers, Available online at
 http://arxiv.org/abs/0902.2524. INEQUALITIES FOR POLYGAMMA FUNCTIONS 11
"... Abstract. In this paper, two sharp inequalities for bounding the psi function ψ and the harmonic numbers Hn are established respectively, some results in [I. Muqattash and M. Yahdi, Infinite family of approximations of the Digamma function, Math. Comput. Modelling 43 (2006), 1329–1336.] are improved ..."
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Cited by 12 (7 self)
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Abstract. In this paper, two sharp inequalities for bounding the psi function ψ and the harmonic numbers Hn are established respectively, some results in [I. Muqattash and M. Yahdi, Infinite family of approximations of the Digamma function, Math. Comput. Modelling 43 (2006), 1329–1336.] are improved, and some remarks are given. 1.
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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Cited by 10 (6 self)
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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.
REFINEMENTS OF LOWER BOUNDS FOR POLYGAMMA FUNCTIONS
, 903
"... Abstract. In the paper, some lower bounds for polygamma functions are refined. 1. Introduction and ..."
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Cited by 9 (6 self)
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Abstract. In the paper, some lower bounds for polygamma functions are refined. 1. Introduction and
Some properties of the psi and polygamma functions
, 2009
"... In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized. ..."
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Cited by 8 (7 self)
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In this paper, some monotonicity and concavity results of several functions involving the psi and polygamma functions are proved, and then some known inequalities are extended and generalized.
AN ALTERNATIVE PROOF OF ELEZOVIĆGIORDANOPEČARIĆ’S THEOREM
, 903
"... Abstract. In the present note, an alternative proof is supplied for Theorem 1 ..."
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Cited by 5 (5 self)
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Abstract. In the present note, an alternative proof is supplied for Theorem 1
Integral representations and complete monotonicity related to the remainder of Burnside’s formula for the gamma function
 Journal of Computational and Applied Mathematics 268 (2014), 155–167; Available online at http://dx.doi.org/10.1016/j.cam.2014.03.004
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Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to ElezovićGiordanoPečarić’s theorem
 J. Inequal. Appl
"... Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or qgamma functions, the logarithmically complete mon ..."
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Cited by 4 (4 self)
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Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or qgamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two gamma functions and divided differences of polygamma functions, and related monotonicity results.