Results 31 to 40 of about 338 (116)

Sharp inequalities related to the constant e

Journal of Inequalities and Applications, 2014
The aim of this work is to extend the results obtained by Batir and Cancan in (Int. J. Math. Educ. Sci. Technol. 40(8):1101-1109, 2009).MSC:26A09, 33B10, 26D99.
Yue Hu, C. Mortici
semanticscholar   +2 more sources

Umbral Methods and Harmonic Numbers

Axioms, 2018
The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli, Bruna Germano, Silvia Licciardi, Maria Renata Martinelli   +3 more
doaj   +1 more source

Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

, 2012
In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving the ...
Andrews, Bai-Ni Guo, Feng Qi, Koumandos, Qi, Qi   +5 more
core   +1 more source

The monotonicity of ratios involving arc tangent function with applications

Open Mathematics, 2019
In this paper, we investigate the monotonicity of the ...
Yang Zhen-Hang, Tin King-Fung, Gao Qin
doaj   +1 more source

Limit formulas for ratios of polygamma functions at their singularities

, 2012
In the paper the author presents limit formulas for ratios of polygamma functions at their singularities.Comment: 4 ...
Qi, Feng
core   +2 more sources

Further results on the neutrix composition of distributions involving the delta function and the function cosh+-1(x1/r+1)$\cosh _ + ^{ - 1}\left( {{x^{1/r}} + 1} \right)$

Demonstratio Mathematica, 2019
The neutrix composition F(f (x)) of a distribution F(x) and a locally summable function f (x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f (x))} is equal to h(x), where Fn(x) = F(x) * δn(x) and {δn(x)}
Fisher Brian, Tas Kenan
doaj   +1 more source

Sharp bounds for Seiffert mean in terms of weighted power means of arithmetic mean and geometric mean

, 2014
For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively.
Zhen-Hang Yang
semanticscholar   +1 more source

Sharpening and generalizations of Shafer's inequality for the arc tangent function

, 2009
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function.
Bai-Ni Guo, Feng Qi, Shi-Qin Zhang
core   +4 more sources

Monotonicity, convexity, and Maclaurin series expansion of Qi's normalized remainder of Maclaurin series expansion with relation to cosine

Open Mathematics
In this article, the authors introduce Qi’s normalized remainder of the Maclaurin series expansion of Qi’s normalized remainder for the cosine function.
Pei Wei-Juan, Guo Bai-Ni
doaj   +1 more source

Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function

Demonstratio Mathematica
In this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
doaj   +1 more source