[PDF] Top 20 Two Logarithmically Completely Monotonic Functions Connected with Gamma Function

... the functions x α |ψ (i) (1 + x)| are strictly increasing in (0, ∞) if and only if α ≥ ...the functions x 2i ψ (2i) (1 + x) and x 2i+1 ψ (2i) (1 + x) are decreasing and the functions x 2i−1 ψ (2i−1) ... 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

... 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 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

... of functions which involve the psi function ψ and the ratio Γ(x+s) Γ(x+t) are logarithmically completely monotonic are established, the best bounds for the ratio Γ(x+s) Γ(x+t) are ... See full document

... condition, logarithmically completely mono- tonic function, Gautschi’s double inequality, Kershaw’s double inequality, Wendel’s double in- equality, ratio of gamma functions, elementary ... 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

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

... [13] F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Austral. Math. Soc. Ser. A (2004), in press. RGMIA Res. Rep. ... See full document

... these functions to complex variables and for basic properties, see ...These functions play central roles in the theory of special functions and have lots of extensive applications in many branches, ... 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

... Guo, S, Qi, F, Srivastava, HM: A class of logarithmically completely monotonic functions related to the gamma function with applications.. Integral Transforms Spec.[r] ... See full document

... “logarithmically 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

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

... For more information on bounding Gurland’s ratio, please refer to 20, 44, 96, 97 and related references therein. However, there does not exist a general identity similar to 3.12 between Gurland’s ratio and the ratio of ... See full document

... In this paper, Theorem 1.1 gives necessary and sufficient conditions for α ∈ R such that the function F(x; α, β) is strictly increasing (decreasing) and concave (convex) on (max(0, –β), ∞) for β ∈ (–∞, 0] (β ∈ [1/2, ... See full document

... digamma) function, and ψ (k) (x) (k ∈ N ) are called polygamma ...These functions play an important role in various branches of mathematics as well as in physics and engi- ...these functions, please ... See full document

... 6. Smith, WD: The gamma function revisited. http://schule.bayernport.com/gamma/gamma05.pdf (2006) 7. Nemes, G: New asymptotic expansion for the gamma function. Arch. Math. (Basel) 95, ... See full document