[PDF] Top 20 Monotonicity and inequalities for the gamma function

... 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

... [5] Ch.-P. Chen and F. Qi, Monotonicity results for the gamma function, J. Inequal. Pure Appl. Math. 3 (2003), no. 2, Art. 44. Available online at http://jipam.vu.edu.au/v4n2/065_02. html. RGMIA Res. ... See full document

... Abstract. In the article, sufficient and necessary conditions that a class of functions involving ratio of Euler’s gamma functions and originating from Wendel-Gautschi-Kershaw’s double inequalities are ... See full document

... integral inequalities with the non-homogeneous kernel and parameters are obtained by Theorem , ...the gamma function are proved to be the best ...main inequalities with the best possible ... See full document

... on inequalities for the gamma and q-gamma func- ...these inequalities follow from the monotonicity properties of functions which are closely related to ... See full document

... the gamma and incomplete gamma functions with usual ...some monotonicity results and inequalities for the gamma or incomplete gamma functions are deduced or extended, a unified ... See full document

... the gamma and the incomplete gamma functions, respec- ...some monotonicity results for the gamma function and extend, to x > 0, a lower bound established by Elbert and Laforgia ... See full document

... In Sect. 2, we prepare two lemmas. In Sect. 3, we discuss applications of some integral inequalities such as Chebychev’s integral inequality. In Sect. 4, we prove the logarithmic convexity of the extended ... 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 ... See full document

... We established a concave theorem and some monotonic properties for the generalized digamma function, and some interesting inequalities were obtained. These conclusions generalize Alzer’s results. On the ... See full document

... the function f  (x)/g  (x) is strictly increasing on (, ...the monotonicity of the function f  (x)/g  (x) on the interval (, ∞ ) and f  ( ∞ ) = g  ( ∞ ) = ... See full document

... Case : a ≤ min { , p/(p + ) } . From p =  and (.) we know that h (u) is strictly increas- ing on (, ∞ ). Then (.), (.), and (.) lead to the conclusion that f (x)/I p (x) is strictly increasing on (, ∞). ... 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, ... See full document

... Remark 2.7.2. Except Wendel’s result, all inequalities above take values on N, the set of positive integers. In other words, only Wendel’s double inequality (2.6), the earliest result on this topic, takes values ... See full document

... p, q ∈ R , a > , b >  } and strictly increasing with respect to its parameters p, q ∈ R for fixed a, b >  with a = b. Many bivariate means are particular cases of the Stolarksy mean, and many remarkable ... See full document

... or gamma function can be found in [16, 18–27] and the references cited ...nice inequalities be- tween gamma function and the truncations of its asymptotic series can be found in [28, ... See full document

... 53. Nemes, G: More accurate approximations for the gamma function. Thai J. Math. 9, 21-28 (2011) 54. Nemes, G: New asymptotic expansion for the Gamma function. Arch. Math. (Basel) 95, 161-169 ... See full document

... Mortici, C, Qi, F: Asymptotic formulas and inequalities for the gamma function in terms of the tri-gamma function.. Luke, YL: The Special Functions and Their Applications, Vol.[r] ... See full document

... J. Chen, A complete monotonicity property of the gamma function, J. Guo, Complete monotonicities of functions involving the gamma and digamma. functions, RGMIA Res. Chen, Some completely[r] ... See full document

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