ratio of gamma functions
Some inequalities for the ratio of gamma functions
... In this paper, we present some sharp inequalities for the ratio of gamma functions. The main tool is the multiple-correction method formulated in (Cao et al. in J. Number Theory 149:327-350, 2015; ...
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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
... of functions involving ratio of Euler’s gamma functions and originating from Wendel-Gautschi-Kershaw’s double inequalities are logarithmically completely monotonic are ...
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Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović Giordano Pečarić’s theorem
... the ratio of two gamma functions, along one of the main lines of bounding the ratio of two gamma functions, the authors look back and analyze some known results, including ...
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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 values on (0, ...
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Bounds for the Ratio of Two Gamma Functions
... 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 ...
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An asymptotic expansion for a ratio of products of gamma functions
... The asymptotic expansion for a ratio of products of gamma functions in this form (2.7) or the other (2.5) seems to be new. It is only the special case when c = 1 which is known. This special case was ...
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Some Inequalities Involving the Geometric Mean of Natural Numbers and the Ratio of Gamma Functions
... In this article, using Stirling’s formula, the series-expansion of digamma functions and other techniques, two inequalities involving the geo- metric mean of natural numbers and the rati[r] ...
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Refinements, Extensions and Generalizations of the Second Kershaw's Double Inequality
... conditions that a class of functions involving ratio of gamma functions are logarithmically completely monotonic , RGMIA Res. Chen, The best bounds in Gautschi-Kershaw inequalities , Mat[r] ...
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Inequalities and asymptotic expansions associated with the Wallis sequence
... We present the asymptotic expansions of functions involving the ratio of gamma functions and provide formulas for determining the coefficients of the asymptotic expansions. As consequences, we ...
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Bounds for triple gamma functions and their ratios
... the ratio of 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 ...
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On complete monotonicity for several classes of functions related to ratios of gamma functions
... of functions involving the ratio of two gamma functions were ...of functions involving the ratio of two gamma functions, including some relating to the Catalan ...
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Monotonicity Results and Inequalities for the Gamma and Incomplete Gamma Functions
... the gamma and incomplete gamma functions with usual ...the gamma or incomplete gamma functions are deduced or extended, a unified proof of some known results for the gamma ...
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Monotonicity and Logarithmic Convexity for a Class of Elementary Functions Involving the Exponential Function
... 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] ...
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Certain Logarithmically N-Alternating Monotonic Functions Involving Gamma and q-Gamma Functions
... monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are ob- tained in ...involving gamma and psi ...
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Complete Monotonicities of Functions Involving the Gamma and Digamma Functions
... In [3] and [4, p. 83], the following result was given: Let f and g be functions such that f ◦ g is defined. If f and g 0 are completely monotonic, then f ◦ g is also completely monotonic. Thus, from Theorem 1 and ...
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The general chain transform and self reciprocal functions
... Parseval theorem, kernel functions, L2-space, self-reciprocal functions, gamma ]’unction, Riemann-Zeta function, Bessel functions, Whittaker functions.. The standard and the simplest def[r] ...
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Some Completely Monotonic Functions Involving the Gamma and Polygamma Functions
... [4] F. Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Res. Available online at http://rgmia. Qi) Department of Applied Mathematics and Informa[r] ...
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Logarithmically Completely Monotonic Functions Involving Gamma and Polygamma Functions
... monotonic functions is the connection between infinitely divisible probability distributions (measure) on R and [0, ∞) and completely monotonic functions related to their Fourier and Laplace ...monotonic ...
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Four Logarithmically Completely Monotonic Functions Involving Gamma Function and Originating from Problems of Traffic Flow
... monotonic functions on I is denoted by ...monotonic functions on (0, ∞) can be characterized as the infinitely divisible completely monotonic functions studied by Horn in [8, Theorem ...
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Completely Monotonic Functions Related to the Gamma Functions
... If the inequality (1) is strict, then f is said to be strictly completely monotonic on I. Completely monotonic functions have remarkable applications in different branches. For instance, they play a role in ...
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