Results 51 to 60 of about 539 (144)
, 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
Journal of King Saud University: Science, 2023 The discrete analysed fractional operator technique was employed to demonstrate positive findings concerning the Atangana-Baleanu and discrete Caputo-Fabrizo fractional operators.
Pshtiwan Othman Mohammed +5 more
doaj
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 +3 more
doaj +1 more source
Estimates for the arctangent function related to Shafer's inequality
, 2014 The aim of this article is to give new refinements and sharpenings of Shafer’s inequality involving the arctangent function. These are obtained by means of a suitable change of variables which makes the computations much easier than the classical ...
C. Mortici, H. Srivastava
semanticscholar +1 more source
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.
core +2 more sources
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
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
Basis properties of p-exponential function of Lindqvist and Peetre type
, 2018 We show that a p -exponential function defined by the p -trigonometric functions of Lindqvist and Peetre form a basis in the Lebesgue space Lr ( (−1,1)n for any r ∈ (1,∞) , provided n 3 and p > pn 1 .
Özlem Baksi +3 more
semanticscholar +1 more source
Finite trigonometric sums arising from Ramanujan's theta functions [PDF]
arXiv, 2022 Two classes of finite trigonometric sums, each involving only $\sin$'s, are evaluated in closed form. The previous and original proofs arise from Ramanujan's theta functions and modular equations.
arxiv
Generalizations of the Bell Numbers and Polynomials and Their Properties
, 2017 In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of ...
Feng Qi (祁锋) +3 more
semanticscholar +1 more source