[PDF] Top 20 Monotonicity properties of a function involving the psi function with applications

... gamma function and psi function ψ have been the subject of intensive ...and monotonicity proper- ties for these functions can be found in the literature ... See full document

... As an important role played in many branches, such as mathematical physics, proba- bility, statistics, and engineering, the gamma and polygamma functions have attracted the attention of many scholars. Recently, many ... See full document

... gamma function Γ(x) is one of the most important special functions and has much extensive applications in many branches, for example, statistics, physics, engineering, and other mathematical ... See full document

... basic properties see 1 . In recent years, many monotonicity results and inequalities involving the Gamma and incomplete Gamma functions have been ... See full document

... a monotonicity property for the function involving the strongly convex function, prove the classical majorization theorem for majorized n-tuples by using strongly convex functions, give some ... 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 ... See full document

... A function involving the divided differences of the psi function and the polygamma functions is proved to be completely ...the monotonicity and convexity of a function originated ... See full document

... fundamental properties involving the gamma, digamma, and polygamma functions can be found in some books ...useful properties. In particular, some properties such as monotonicity, ... See full document

... [4] F. Qi, Certain logarithmically N-alternating monotonic functions involving gamma and q-gamma functions, Nonlinear Funct. Anal. Appl. (2007), in press. RGMIA Res. Rep. Coll. 8 (2005), no. 3, Art. 5, 413–422; ... See full document

... the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric ...As applications, we find several complete monotonicity properties for ... See full document

... 1-log-convex function (or 1-log-concave function, respectively) is equivalent to a positive and increasing (or decreasing, respectively) function and that a 2-log-convex function is positive ... See full document

... Remark  By a similar approach to that presented in the next section, we can procure similar monotonicity results and inequalities for the inverse hyperbolic cosine and other inverse trigonometric functions. For ... See full document

... monotonic properties for the generalized digamma function, and some interesting inequalities were ...digamma function by using Ismail and Laforgia’s ... See full document

... the monotonicity of the function f ...such monotonicity since the gamma function occurs in denom- ...the monotonicity of such ... See full document

... [1]M. A. Chaudhry, S. M. Zubair, Generalized incomplete gamma functions withapplications,J. Comput. Appl. Math. 55 (1994), 99–124. [2] M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s ... See full document

... 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 the first Kershaw’s double ... See full document

... the function f is said to be subordinate to g or g is said to be superordinate to f , if there exists a function w analytic in U with |w| ≤ |z| such that f (z) = ...the function g is univalent in U , ... See full document

... functions on (0, ∞)(see [3], [9]). Thus, one expects to deduce results on gamma and q-gamma functions from properties of completely monotonic functions, by applying them to functions related to ψ 0 or ψ 0 q . It ... See full document

... 30. Qi, F, Guo, B-N: Sharp inequalities for the psi function and harmonic numbers (2009). arXiv:0902.2524 [math. CA] 31. Guo, B-N, Qi, F: Sharp inequalities for the psi function and harmonic ... See full document

... [39] J. Dutka, On some gamma function inequalities, SIAM J. Math. Anal. 16 (1985), 180–185. [40] L. Durand, Nicholson-type integrals for products of Gegenbauer functions and related topics, in: R.A. Askey (Ed.), ... See full document