We prove the case ρ = 4 of the following conjecture of Koumandos and Ruscheweyh: let s μ n (z) := ∑n k=0 (μ)k k! z k , and for ρ ∈ (0, 1] let μ(ρ) be the unique solution of ∫ (ρ+1)π 0 sin(t − ρπ)tμ−1dt = 0 in (0, 1]. Then we have | arg[(1− z)ρs n (z)]| ≤ ρπ/2 for 0 < μ ≤ μ(ρ), n ∈ N and z in the unit disk of C and μ(ρ) is the largest number with this property. For the proof of this other new re...

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan’s notebooks and were systematically first studied by Berndt and Zaharescu; their proofs involved complex contour integration. We show how to prove most of Berndt–Zaharescu’s and some new identities by elementary metho...

In this paper we study embedding theorems of function classes, which are subclasses of Lp, 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ, β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.

In this article, some fresh solitary and periodic solutions of the Gardner equation have been explored with free parameters via the Exp -function method. The solutions are presented in terms of hyperbolic and trigonometric functions. The solutions and are revealed in figures. The symbolic computation software, such as, Maple 13, make the solution procedure straightforward and concise. AMS subje...

We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbit...

Policy iteration techniques for multiple-server dispatching rely on the computation of value functions. In this context, we consider the M/G/1FCFS queue endowed with an arbitrarily-designed cost function for the waiting times of the incoming jobs, and we study an undiscounted value function integrating the total cost surplus expected from each state relative to the steady-state costs. When coup...

Starting from certain inequalities for hyperbolic and trigonometric functions, we obtain some general inequalities for functions and their inverses. As applications, refinements and new inequalities for hyperbolic and trigonometric functions are pointed out.

Policy iteration techniques for multiple-server dispatching rely on the computation of value functions. In this context, we consider continuous-space M/G/1-FCFS queue endowed with an arbitrarily designed cost function waiting times incoming jobs. The associated relative is a solution Poisson’s equation Markov chains, which in work solve Laplace transform domain by considering ancillary, underly...

When we fix one side and draw different tangential quadrilaterals having the same side lengths but different angles we observe that their incenters lie on a circle. Based on a known formula expressing the incircle radius of a tangential quadrilateral by its tangent lengths, some older results will be presented in a new light and the equation of the before mentioned circle will appear. This circ...