Results 61 to 70 of about 539 (144)

From a cotangent sum to a generalized totient function

, 2017
In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{\pi m}{b}\right)\sin^{3}\left(2\pi m\frac{a}{b}\right)\:$$ and associate the distribution of its values to a generalized ...
Rassias, Michael Th.
core   +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

Some Analytical Properties of the Hyperbolic Sine Integral [PDF]

arXiv, 2023
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational bounds for the hyperbolic tangent function.
arxiv  

New inequalities and infinite product formulas for trigonometric and the lemniscate functions

, 2015
In this paper, we give a new approach to prove inequalities for the Schwab-Borchardt mean, the lemniscatic mean and the arithmetic geometric mean. Additionally, we apply these means to inequalities for trigonometric functions or the lemniscate functions ...
R. Nishimura
semanticscholar   +1 more source

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

An analysis of exponential kernel fractional difference operator for delta positivity

Nonlinear Engineering
Positivity analysis for a fractional difference operator including an exponential formula in its kernel has been examined. A composition of two fractional difference operators of order (ν,μ)\left(\nu ,\mu ) in the sense of Liouville–Caputo type operators
Mohammed Pshtiwan Othman
doaj   +1 more source

On some convergences to the constant e and improvements of Carlemans' inequality [PDF]

arXiv, 2013
We present inequalities and some applications to Kellers' limit and Carlemans' inequality.
arxiv  

Some inequalities and an application of exponential polynomials

, 2020
In the paper, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, the author presents an explicit formula and an identity for ...
Feng Qi (祁锋)
semanticscholar   +1 more source

New Upper Bounds in the Second Kershaw's Double Inequality and its Generalizations [PDF]

, 2007
In the paper, new upper bounds in the second Kershaw’s double inequality and its generalizations involving the gamma, psi and polygamma functions are established, some known results are ...
Guo, Senlin, Qi, Feng
core  

Remarks on trigonometric functions after Eisenstein [PDF]

arXiv, 2016
We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function $\varepsilon_2$.
arxiv