Results 11 to 20 of about 338 (116)
Monotonicity results and bounds for the inverse hyperbolic sine [PDF]
Journal of Inequalities and Applications, 2009 In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine.
B-N Guo +14 more
core +4 more sources
Three families of two-parameter means constructed by trigonometric functions
Journal of Inequalities and Applications, 2013 In this paper, we establish three families of trigonometric functions with two parameters and prove their monotonicity and bivariate log-convexity. Based on them, three two-parameter families of means involving trigonometric functions, which include ...
Zhen-Hang Yang
semanticscholar +2 more sources
Geometric convexity of the generalized sine and the generalized hyperbolic sine [PDF]
, 2013 In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively.
Jiang, Wei-Dong, Qi, Feng
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Diagonal recurrence relations for the Stirling numbers of the first kind [PDF]
, 2015 In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 ...
Qi, Feng
core +3 more sources
On the Fresnel sine integral and the convolution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 37, Page 2327-2333, 2003., 2003 The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S+(x), S−(x), C+(x), and C−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x+r, xr are evaluated.
Adem Kılıçman
wiley +1 more source
Some properties of the generalized Gaussian ratio and their applications
, 2020 We are devoted to an integral, asymptotic expansion and Maclaurin series representation for the generalized Gaussian ratio, and find their various related properties such as complete monotonicity and some useful inequalities.
Zhen-Hang Yang, B. Xi, Shenzhou Zheng
semanticscholar +1 more source
On the Fresnel integrals and the convolution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 41, Page 2635-2643, 2003., 2003 The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x+r and xr are evaluated.
Adem Kiliçman, Brian Fisher
wiley +1 more source
On some trigonometric power sums
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 3, Page 185-191, 2002., 2002 Using the generating function method, the closed formulas for various power sums of trigonometric functions are established. The computer algebra system Maple is used to carry out the complex calculations.
Hongwei Chen
wiley +1 more source
A survey for generalized trigonometric and hyperbolic functions
Journal of Mathematical Inequalities, 2019 The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2012, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and ...
L. Yin +3 more
semanticscholar +1 more source
Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]
, 2012 In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
core +1 more source