[PDF] Top 20 A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function

... 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

... 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

... 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

... 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

... 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

... where 0 < s < 1, x ≥ 1, Γ is the classical Euler’s gamma function, and ψ is the logarithmic derivative of Γ. They are called the first and second Kershaw’s double inequality respectively. There have ... See full document

... phrases. logarithmically completely monotonic function, completely monotonic function, gamma function, psi function, ... See full document

... HL: Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler’s gamma ...q-Zeta Functions and ... 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 ... See full document

... special functions [1, 14, 15] and has much extensive applications in many branches, for example, statistics, physics, engineering, and other mathematical ... See full document

... measure µ in (1) is infinitely divisible in the convolution sense: For each n ∈ N there exists a positive measure ν on [0, ∞) with n-th convolution power equal to µ. By the way, recall [30, 32, 48, 52, 54] that a ... See full document

... “logarithmically completely monotonic function” was introduced by ...the class of logarithmically completely monotonic functions is a subclass of ... See full document

... numerous functions, which are defined in terms of gamma, polygamma, and other special functions, are (logarithmically) completely monotonic and used this fact to derive many ... 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

... [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

... [2] 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 completely monotonic functions and the logarithmically completely monotonic functions on I are denoted respectively by C[I] and ... 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

... Hence, p 00 (t) increases in (0, ∞). Since p 00 (0) = 3 > 0, we have p 00 (t) > 0 and p 0 (t) is increasing. Because of p 0 (0) = 0, it follows that p 0 (t) > 0 in (0, ∞), and then p(t) is increasing. From p(0) ... See full document

... The completely monotonic functions are useful in various branches, including mathematical analysis, probability theory and numerical ...the gamma and various related ...the function θ( ... See full document