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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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Cited by 7 (7 self)
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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.
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 2 (2 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.