Results 41 to 50 of about 266 (93)
Some new inequalities for trigonometric functions and corresponding ones for means [PDF]
arXiv, 2013 In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
arxiv
Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach. [PDF]
Heliyon, 2023 Mahmood A +6 more
europepmc +1 more source
On the conjecture of generalized trigonometric and hyperbolic functions [PDF]
arXiv, 2014 In this paper we prove the conjecture posed by Kl\'en et al. in \cite{kvz}, and give optimal inequalities for generalized trigonometric and hyperbolic functions.
arxiv
Logarithmic mean inequality for generalized trigonometric and hyperbolic functions [PDF]
arXiv, 2014 In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.
arxiv
On the generalized convexity and concavity [PDF]
arXiv, 2014 In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.
arxiv
A Short Proof of a Concrete Sum [PDF]
arXiv, 2016 We give an alternative proof of a formula that generalizes Hermite's identity. Instead involving modular arithmetic, our short proof relies on the Fourier-type expansion for the floor function and on a trigonometric formula.
arxiv
Evaluations of Series of Hyperbolic Functions [PDF]
arXiv, 2017 In this article we give evaluations of certain series of hyperbolic functions, using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
arxiv
On a finite trigonometric sum related to Dedekind sum [PDF]
arXiv, 2018 Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric functions.
arxiv
A pair of optimal inequalities related to the error function [PDF]
arXiv, 1997 The Error Function \begin{eqnarray} V(x) & \equiv & \sqrt{\pi} e^{x^2} [1 - \hbox{erf}(x)] \\ & = & \int_0^\infty \frac{ e^{-u} }{\sqrt{x^2 + u}} du = 2 e^{x^2}\int_x^\infty e^{-t^2} dt \nonumber \end{eqnarray} arises in many contexts, from probability to mathematical physics.
arxiv
arXiv, 2004 This is a translation into English from the original Latin of Leonhard Euler's Exercitatio analytica, Nova Acta Academiae Scientarum Imperialis Petropolitinae 8 (1794), 69-72; E664 in the Enestrom index. In it Euler uses the infinite product identity for sin to prove some properties of the series for the Riemann zeta function for even n.
arxiv