[PDF] Top 20 Three Classes of Logarithmically Completely Monotonic Functions Involving Gamma and Psi Functions

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

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

... (1) for 0 < s < 1 and x ≥ 1, where Γ denotes the classical Euler’s gamma function and the middle term in (1) is a special case of the Wallis’ function Γ(x+p) Γ(x+q) for x + p > 0 and x + q > 0. It is ... See full document

... the gamma, psi and polygamma functions, and other analytic ...(logarithmically) completely monotonicity re- sults related to Ψ s,t (x) and Gautschi-Kershaw inequalities (1) and (2) are ... 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

... the functions involving R(x) = ψ (x + 1/2) – ln x with a parameter are completely monotonic on (0, ∞), find three new sequences which are fast convergence toward the Euler-Mascheroni ... See full document

... [17] F. Qi, A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, Comput. Math. Appl. (2006), accepted. ... See full document

... deduced functions involving the gamma and psi func- tions are proved to be decreasingly monotonic and logarithmically completely monotonic, and some remarks and ... 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

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

... the logarithmically complete monotonicity of ratios of two gamma functions is closely related to the divided difference of psi and polygamma ... 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, and ... See full document

... [14] F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Austral. Math. Soc. 79 (2006), no. 1, in press. RGMIA ... See full document

... conditions that a class of functions involving ratio of gamma functions are logarithmically completely monotonic , RGMIA Res. Chen, The best bounds in Gautschi-Kershaw inequalities , Mat[r] ... See full document

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

... the completely monotonic or logarithmically completely monotonic func- tions have been the subject of intensive ...or logarithmically complete monotonicity involving the ... 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

... [26] F. Qi, A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, Comput. Math. Appl. (2007), in press. ... 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 ... See full document

... [1] M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 edition. A Wiley-Interscience Pub- lication. Selected Government ... See full document