Results 21 to 30 of about 338 (116)

On the sine integral and the convolution

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 365-375, 2002., 2002
The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
Brian Fisher, Fatma Al-Sirehy
wiley   +1 more source

Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications

, 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

On New Inequalities Involving Circular, Inverse Circular, Inverse Hyperbolic and Exponential Functions

, 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, Sumedh B. Thool, R. Dhaigude   +2 more
semanticscholar   +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

On transcendental numbers

, 2014
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them.
Nichita, Florin F.
core   +2 more sources

Derivative Polynomials and Closed-Form Higher Derivative Formulae [PDF]

, 2009
In a recent paper, Adamchik [V.S. Adamchik, On the Hurwitz function for rational arguments, Appl. Math. Comp. 187 (2007) 3--12] expressed in a closed form symbolic derivatives of four functions belonging to the class of functions whose derivatives are ...
Cvijović, Djurdje
core   +2 more sources

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

Some results on hybrid relatives of the Sheffer polynomials via operational rules

Miskolc Mathematical Notes, 2019
The intended objective of this paper is to introduce a new class of polynomials, namely the extended Laguerre-Gould-Hopper-Sheffer polynomials. The generating function and operational rule are derived by making use of integral transform.
Mahvish Ali, Tabinda Nahid, Subuhi Khan
semanticscholar   +1 more source