[PDF] Top 20 Some inequalities for the gamma k-function
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Some inequalities for the gamma k-function
... defined k-hypergeometric differential equation and gave twenty four solutions of said k-hypergeometric differential ...generalized gamma k-function and discussed the following ... See full document
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7. Some Results on a Generalized Hypergeometric $k$-Functions
... special k-functions like gamma k- function, beta k-function, hypergeometric k-function, solutions of hypergeometric k-differential equations, contiguous ... See full document
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Sharp Smith’s bounds for the gamma function
... As a consequence, we get some new sharp estimates to various classical inequalities concerning the gamma function and hyperbolic functions.... Acknowledgements This paper is supported by[r] ... See full document
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Some inequalities involving k gamma and k beta functions with applications II
... of k-special functions like the k-gamma function, the k-polygamma function, the k-beta function, the k-hypergeometric functions, solutions of ... See full document
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Some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k function
... present some inequalities involving the extended gamma function and the Kummer confluent hypergeometric k-function via some classical inequalities such as ... See full document
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Certain Inequalities for the Conformable Gamma and Polygamma Functions
... classical Gamma function which they called, the conformable Gamma ...establish some inequalities for the conformable Gamma and Polygamma ...of some classical ... See full document
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Monotonicity and inequalities for the gamma function
... Remark 3 In this paper, we investigate the monotonicity of the function f (x). In general, it is difficult to deal with such monotonicity since the gamma function occurs in denom- inator. However, by ... 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- ...prove some monotonicity results for the gamma function and extend, to x > 0, a lower bound established by Elbert and Laforgia ... See full document
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Some inequalities for the ratio of gamma functions
... Let us briefly review the so-called multiple-correction method presented in our previous papers [, ]. Actually, the multiple-correction method is a recursive algorithm, and one of its advantages is that by repeating ... 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. ... See full document
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Monotonicity of the incomplete gamma function with applications
... Gupta, SS, Waknis, MN: A system of inequalities for the incomplete gamma function and the normal integral.. Yamagata, K: A contribution to the theory of non-isothermal laminar flow of flui[r] ... See full document
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Bounds for triple gamma functions and their ratios
... section, some inequalities for 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 ... See full document
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Best constants for certain multilinear integral operators
... revisit some important inequalities due to Hilbert, Hardy- Littlewood-P ´olya, and ...these inequalities and provide formulas for the best constants in a closed form via the gamma ...the ... See full document
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Improvements of the bounds for Ramanujan constant function
... n k= /k – logn) = ...the gamma and psi functions have many applications in the areas of mathematics, physics, and engineering ...the gamma and psi functions have attracted the interest of ... See full document
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Approximation for the gamma function via the tri gamma function
... 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
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Padé approximant related to asymptotics for the gamma function
... Gamma function. Arch. Math. (Basel) 95, 161-169 (2010) 55. Alzer, H: On some inequalities for the gamma and psi ...on some completely monotonic ... See full document
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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 ... See full document
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Two double inequalities for k gamma and k Riemann zeta functions
... 3. Nguyen, VV, Ngo, PNN: An inequality for the gamma function. Int. Math. Forum 4(28), 1379-1382 (2009) 4. Díaz, R, Pariguan, E: On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. ... See full document
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On Hardy type integral inequalities with the gamma function
... integral inequalities with the non-homogeneous kernel and ...the gamma function are proved to be the best ...and some cases of homogeneous ... See full document
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Monotonicity and inequalities involving the incomplete gamma function
... Case : a ≥ . Then from (.)-(.) we clearly see that the function f (x)/g (x) is strictly increasing on (, ∞). Therefore, R(x) is strictly increasing on (, ∞) follows from Lemma . and (.) together ... See full document
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