Two-Sided Inequality Involving the q-Gamma Function

被引:0
作者
Salem A. [1 ]
Alzahrani F. [1 ]
机构
[1] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah
关键词
Completely monotonic function; Inequalities; q-Gamma function; q-Polygamma functions;
D O I
10.1007/s40819-017-0476-4
中图分类号
学科分类号
摘要
An inequality involving the q-gamma and q-trigamma functions is derived and proved for all real number q> 0. This inequality provides new bounds for the q-gamma function in terms of the q-trigamma function. © 2017, Springer (India) Private Ltd., part of Springer Nature.
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共 15 条
[1]  
Salem A., Two classes of bounds for the q -gamma and the q -digamma functions in terms of the q -zeta functions, Banach J. Math. Anal., 8, 1, pp. 109-117, (2014)
[2]  
Batir N., On some properties of the gamma function, Expo. Math., 26, pp. 187-196, (2008)
[3]  
Yu Y., A remark on a class of double inequalities of Batir, Expo. Math., 27, pp. 171-174, (2009)
[4]  
Abramowitz M., Stegun C.A., Handbook of Mathematical Functions with Formulas, Graphs, Mathematical Tables 7Th Printing, Applied Mathematics Series, 55, (1964)
[5]  
Askey R., The q -gamma and q -beta functions, Appl. Anal., 8, pp. 125-141, (1978)
[6]  
Moak D.S., The q -gamma function for q> 1, Aequ. Math., 20, pp. 278-285, (1980)
[7]  
Moak D.S., The q -analogue of Stirling’s formula, Rocky Mt. J. Math., 14, pp. 403-413, (1984)
[8]  
Daalhuis O., Asymptotic expansions of q -gamma, q -exponential and q -bessel functions, J. Math. Anal. Appl., 186, pp. 896-913, (1994)
[9]  
Salem A., Alzahrani F., Improvements of bounds for the q -gamma and the q -polygamma functions, J. Math. Ineq., 11, 3, pp. 873-883, (2017)
[10]  
Salem A., A certain class of approximations for the q -digamma function, Rocky Mt. J. Math., 46, 5, pp. 1665-1677, (2016)