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A Double Inequality for Gamma Function
... Recently, the gamma function has been the subject of intensive research, many remarkable inequalities for Γ can be found in literature 2–21. In particular, the ratio Γs/Γrs > r > 0 have attracted the ... See full document
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Bounds for the Ratio of Two Gamma Functions
... 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 ... See full document
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A Class of Logarithmically Completely Monotonic Functions and the Best Bounds in the First Kershaw's Double Inequality
... Euler’s gamma function are proved, a class of the first Kershaw type double inequalities are established, and the first Kershaw’s double inequality and Wendel’s inequality are ... See full document
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Wendel-Gautschi-Kershaw's Inequalities and Sufficient and Necessary Conditions that a Class of Functions Involving Ratio of Gamma Functions are Logarithmically Completely Monotonic
... Wendel-Gautschi-Kershaw’s double inequali- ties from (1) to (5) and Gautschi-Kershaw’s double inequality (25), for examples, [3, 5, 10, 15, 12, 26, 36, 41] and the references ... See full document
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On a Result of Hardy and Ramanujan
... [4] Necdet Batir, An Interesting Double Inequality for Euler’s Gamma Function, JIPAM , 5 (4) (2004), Article 97. (submitted for publication) [10] Melvyn B[r] ... See full document
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An inequality for the gamma function via statistics and applications
... of gamma functions in the liter- ature; see ...an inequality satisfied by the gamma function, using the so-called Cramér-Rao lower bound for the variance of unbiased ...another ... See full document
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A Class of Logarithmically Completely Monotonic Functions and the Best Bounds in the Second Kershaw's Double Inequality
... the function h(x) is convex if i = 0 or concave if i ≥ ...of inequality (38) (or reversed inequality of (38), respectively) are satisfied by f (x) = (−1) i ψ (i) (x) and g(x) = 1 ... See full document
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New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations
... function on an interval I must be completely monotonic on I. The logarithmically completely monotonic functions have close relationships with both the completely monotonic functions and Stieltjes transforms. For ... See full document
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Bounds for triple gamma functions and their ratios
... the double gamma functions and the triple gamma functions are obtained with the help of the series representation of di-double gamma and di-triple gamma ... See full document
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Four Logarithmically Completely Monotonic Functions Involving Gamma Function and Originating from Problems of Traffic Flow
... Inequalities (9) and (10) extend (4) and (5) and the right hand side inequality of (9) refines the right hand side inequality of (4) and (5). Therefore, it can be said that Theorem 1 generalizes, extends, ... See full document
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A Completely Monotonic Function Involving Divided Difference of Psi Function and an Equivalent Inequality Involving Sum
... [13] F. Qi, B.-N. Guo, and Ch.-P. Chen, Some completely monotonic functions involving the gamma and polygamma functions, J. Austral. Math. Soc. 80 (2006), 81–88. RGMIA Res. Rep. Coll. 7 (2004), no. 1, Art. 5, ... See full document
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About some exponential inequalities related to the sinc function
... 3.2 Inequalities with polynomial exponents In this subsection, we propose and prove a new double-sided inequality involving the sinc function with polynomial exponents.. To be more speci[r] ... See full document
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The Best Bounds in Kershaw's Inequality and Two Completely Monotonic Functions
... other analytic techniques. Recently the paper [16] by S. Koumandos applied the monotonicity results in Theorem 1 to obtain an inequality which generalizes the sharpened Wallis’ double inequality ... See full document
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New series involving the zeta function
... In [2, 3] Choi, Srivastava, and Quine used the theory of the double gamma function to evaluate some series associated with the zeta function. Now in the present paper, we use the property of ... See full document
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Sharpening and Generalizations of Shafer's Inequality for the Arc Tangent Function
... For possible applications of the double inequality 2.11 in the theory of approximations, the accuracy of bounds in 2.11 for the arc tangent function is described by Figures 1 and 2.... J[r] ... See full document
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Fourier transform and distributional representation of the gamma function leading to some new identities
... the gamma functions, which leads natu- rally to a distributional representation for ...of gamma functions multiplied by other functions, which are also presented ... See full document
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An Optimal Double Inequality for Means
... Chen, “The monotonicity of the ratio between generalized logarithmic means,” Journal of Mathematical Analysis and Applications, vol.. Chen, “Refinements, extensions and generalizations o[r] ... See full document
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A Double Inequality for the Ratio of Two Consecutive Bernoulli Numbers
... [12] J. Higgins, Double series for the Bernoulli and Euler numbers, J. London Math. Soc. 2nd Ser. 2 (1970), 722–726; Available online at http://dx.doi.org/10.1112/jlms/2.Part_4.722. [13] S. Jeong, M.-S. Kim, and ... See full document
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A new representation of extended Mittage-Leffler function and its properties
... contains Gamma function, Beta function, Hypergeometric function, Bessel’s function, Mittag-Leffler.. 14.[r] ... See full document
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Supplements to known monotonicity results and inequalities for the gamma and incomplete gamma functions
... the gamma and the incomplete gamma functions, respec- ...the gamma function and extend, to x > 0, a lower bound established by Elbert and Laforgia (2000) for the function ... See full document
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