Results 51 to 60 of about 338 (116)

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

Logarithmic mean inequality for generalized trigonometric and hyperbolic functions [PDF]

, 2014
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.Comment:
Barkat Ali, Bhayo, Li Yin
core  

Derivatives of tangent function and tangent numbers

, 2015
In the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and ...
Bourbaki, Boyadzhiev, Comtet, Daboul, Dominici, Feng Qi, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Hoffman, Hoffman, Luo, Luo, Ma, Ma, Ma, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Remmert, Schwatt, Schwatt, Wei, Xu, Zhang   +37 more
core   +1 more source

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

Oppenheim's problem and related inequalities for Dunkl kernels

, 2014
In this paper, we establish some inequalities related to Oppenheim’s problem for Dunkl kernels. In order to prove our main results, we present new inequalities involving modified Bessel functions of the first kind.
F. Chouchene
semanticscholar   +1 more source

ON THE GENERALIZED FRESNEL SINE INTEGRALS AND CONVOLUTION [PDF]

, 2012
The generalized Fresnel sine integral Sk(x) and its associated functions Sk+(x) ; Sk-(x) are de fined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the generalized Fresnel sine integral and its associated ...
JOLEVSKA-TUNESKA, BILJANA, LAZAROVA, LIMONKA   +1 more
core  

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach. [PDF]

Heliyon, 2023
Mahmood A, Srivastava HM, Abbas M, Abdullah FA, Othman Mohammed P, Baleanu D, Chorfi N.   +6 more
europepmc   +1 more source

The asymptotic expansion of a generalisation of the Euler-Jacobi series [PDF]

, 2015
We consider the asymptotic expansion of the sum Sp(a; w) = ∞Ʃ n=1 e−anp/nw as a → 0 in | arg a| <1/2π for arbitrary finite p > 0 and w > 0. Our attention is concentrated mainly on the case when p and w are both even integers, where the expansion
Paris, Richard B.
core   +2 more sources

On some determinants involving the tangent function

, 2019
Let $p$ be an odd prime and let $a,b\in\mathbb Z$ with $p\nmid ab$. In this paper we mainly evaluate $$T_p^{(\delta)}(a,b):=\det\left[\tan\pi\frac{aj^2+bk^2}p\right]_{\delta\le j,k\le (p-1)/2}\ \ (\delta=0,1).$$ For example, in the case $p\equiv3\pmod4 ...
Sun, Zhi-Wei
core