Results 31 to 40 of about 539 (144)
, 2010 Recently trigonometric inequalities of N. Cusa and C. Huygens (see, e.g., [9]), J. Wilker [11], and C. Huygens [4] have been discussed extensively in mathematical literature.
E. Neuman, J. Sándor
semanticscholar +1 more source
The natural approach of Wilker-Cusa-Huygens inequalities
, 2011 The aim of this paper is to provide a natural approach of Wilker-Cusa-Huygens inequalities. This new approach permits us to give new proofs then to refine much these inequalities and we are convinced that it is suitable to establish many other similar ...
C. Mortici
semanticscholar +1 more source
, 2018 Let Iv (x) be modified Bessel functions of the first kind. We prove the monotonicity property of the function x → Iu (x) Iv (x)/I(u+v)/2 (x) on (0,∞) .
Zhen-Hang Yang, Shenzhou Zheng
semanticscholar +1 more source
, 2020 In this paper, we provide alternative proofs to some results proposed in the article ”New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions” authored by Yogesh J. Bagul.
Yogesh J. Bagul +2 more
semanticscholar +1 more source
On an Umbral point of view to the Gaussian and Gaussian like functions [PDF]
arXiv, 2022 In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are close to Gaussian distribution but have a longer tail. Their use and their link with hypergeometric function is eventually presented.
arxiv
An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers [PDF]
Mediterranean Journal of Mathematics 13 (2016), no. 5, 2795--2800, 2014 In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.
arxiv +1 more source
Optimal inequalities involving power-exponential mean, arithmetic mean and geometric mean
, 2017 For a,b > 0 with a = b , the power-exponential mean is defined by Z ≡ Z (a,b) = exp ( a lna+b lnb a+b ) = √ abe tanht , where t = ln √ a/b . In this paper, we prove the double inequality ( Zp +Gp 2 )1/p < A < ( Zq +Gq 2 )1/q holds for a,b > 0 , a = b ...
Zhen-Hang Yang, Jing-feng Tian
semanticscholar +1 more source
Complete monotonicity and inequalites involving Gurland's ratios of gamma functions
Mathematical Inequalities & Applications, 2019 In this paper, by a comparison inequality for an auxiliary function with two parameters, we present necessary and sufficient conditions for four classes of ratios involving gamma function to be logarithmically completely monotonic. These not only greatly
Zhen-Hang Yang, Shenzhou Zheng
semanticscholar +1 more source
On an open problem of Feng Qi and Bai-Ni Guo
, 2020 In this work, we investigate an open problem posed by Feng Qi and Bai-Ni Guo in their paper ”Complete monotonicities of functions involving the gamma and digamma functions [7]”. Mathematics subject classification (2010): 26A09, 33B10, 26A48.
M. Bouali
semanticscholar +1 more source
Sharp Wilker-type inequalities with applications
Journal of Inequalities and Applications, 2014 In this paper, we prove that the Wilker-type inequality 2k+2(sinxx)kp+kk+2(tanxx)p>(0 or p≤−ln(k+2)−ln2k(lnπ−ln2) (−125(k+2)≤p(
Zhen-Hang Yang, Y. Chu
semanticscholar +2 more sources