Results 31 to 40 of about 316 (101)

On transcendental numbers: new results and a little history

, 2017
Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$ and $\pi$, and
Marcus, Solomon, Nichita, Florin F.
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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.
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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
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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

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

Parametric Fourier and Mellin transforms of power-constructible functions

Forum of Mathematics, Sigma
We enrich the class of power-constructible functions, introduced in [CCRS23], to a class $\mathcal {C}^{\mathcal {M,F}}$ of algebras of functions which contains all complex powers of subanalytic functions and their parametric Mellin and Fourier ...
Raf Cluckers, Georges Comte, Tamara Servi   +2 more
doaj   +1 more source

Certain properties and characterizations of a novel family of bivariate 2D-q Hermite polynomials

Open Mathematics
This study presents a novel family of bivariate 2D-qq Hermite polynomials. We derive explicit forms and qq-partial differential equations and investigate numerical aspects associated with these polynomials.
Wani Shahid Ahmad, Zayed Mohra, Nahid Tabinda   +2 more
doaj   +1 more source

Two-iterated degenerate Appell polynomials: properties and applications

Arab Journal of Basic and Applied Sciences
In the development of hybrid special polynomials, it is essential to incorporate the monomiality principle, operational rules, and other related properties.
Shahid Ahmad Wani
doaj   +1 more source

A generalization of starlike functions of order alpha [PDF]

, 2015
For every $q\in(0,1)$ and $0\le ...
Agrawal, Sarita, Sahoo, Swadesh K.
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