[PDF] Top 20 Monotonic and Logarithmically Convex Properties of a Function Involving Gamma Functions

... digamma functions and other techniques, some monotonicity and logarithmical concavity involving the ratio of gamma function are obtained, which is to give a partially a ffi rmative answer to an ... See full document

... the logarithmically complete monotonicity of a class of functions involving the Euler’s gamma function are proved, a class of the first Kershaw type double inequalities are established, ... See full document

... Zhao, T.-H., Chu, Y.-M.: A class of logarithmically completely monotonic functions associated with a gamma function.. Zhao, T.-H., Chu, Y.-M., Jiang, Y.-P.: Monotonic and logarithmically[r] ... See full document

... of functions involving ratio of Euler’s gamma functions and originating from Wendel-Gautschi-Kershaw’s double inequalities are logarithmically completely monotonic are ... See full document

... completely monotonic on I, then f (x) is called a completely monotonic func- tion of k-th order on an interval ...a logarithmically completely monotonic function is always completely ... See full document

... completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...or logarithmically complete monotonicity involving the gamma, psi ... See full document

... the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and convexity property by ...complete monotonic- ity results on ... See full document

... pletely monotonic function” was introduced explicitly in [9], published formally in [8], and used immediately in [2, 4, 10, 11, ...the logarithmically completely monotonic functions on ... See full document

... these functions to complex variables and for basic proper- ties see ...the gamma function and psi function ψ have been the subject of intensive ...these functions can be found in the ... See full document

... monotonicity properties for the two-parameter hyperbolic and trigonometric ...monotonicity properties for the functions involving the gamma function and provide the bounds for ... See full document

... fundamental properties involving the gamma, digamma, and polygamma functions can be found in some books ...these functions are all key parts of special ...useful properties. In ... See full document

... completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...and logarithmically complete monotonicity properties related to the ... See full document

... a logarithmically completely monotonic function is always completely monotonic, that is, L[I] ⊂ C[I], but not ...that logarithmically completely monotonic functions on (0, ... See full document

... completely monotonic function” was explicitly coined in [2] and recovered in [10, 12, 14] and the following much useful, important and key conclusion was proved: L[I] ⊂ ... See full document

... the logarithmically completely monotonic functions on I is denoted by ...the logarithmically completely monotonic functions on (0, ∞) can be characterized as the infinitely ... See full document

... of functions involving Euler’s gamma function and originating from certain problems of traffic flow are proved to be logarithmically completely monotonic and a class of ... See full document

... 15. Qi, F.: Several integral inequalities. J. Inequal. Pure Appl. Math. 1(2), Article ID 19 (2000) 16. Qi, F., Luo, Q.-M.: Refinements and extensions of an inequality. Math. Inform. Q. 9(1), 23–25 (1999) 17. Tian, J.-F.: ... See full document

... we assume that f 00 (x) is completely monotonic on (0, ∞). This completes the proof. As a direct consequence of Theorem 3.1, we now generalize a result of Alzer[1, Theorem 10], we note here one can also put our ... See full document

... In this paper we establish some inequalities of Hadamard’s type involving Godunova-Levin functions, P-functions, quasi-convex functions, J- quasi-convex functions, Wright-convex function[r] ... See full document

... 2000 Mathematics Subject Classification. Primary 33B15; Secondary 26D07, 26D20. Key words and phrases. Monotonicity, difference, psi function, remainder, inequality. The first author was supported in part by the ... See full document