A class of C rational cubic/linear trigonometric interpolation spline with two local parameters is proposed. Simple sufficient conditions for constructing positivity-preserving interpolation curves are developed. By using the boolean sum of quadratic trigonometric interpolating operators to blend together the proposed rational cubic/linear trigonometric interpolation splines as four boundary fu...

A trigonometric polynomial generalization to the positivity of an alternating sum of binomial coeecients is given. The proof uses lattice paths, and identiies the trigonometric sum as a polynomial with positive integer coeecients. Some special cases of the q-analog conjectured by Bressoud are established, and new conjectures are given.

Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the properties of the generalised functions are discussed. Importance of these functions and their possible applications are also considered. PACS No.: 02.30.Hq, 02.30.Gp...

Schur complements provide a convenient tool for proving the operator valued version of the classical (single variable) Fejér-Riesz problem. It also enables the factorization of multivariable trigonometric polynomials which are strictly positive. A result of Scheiderer implies that in two variables, nonnegative scalar valued trigonometric polynomials have sums of squares decompositions, Using a ...

In this paper some of the results of a recent computer search CoLy99] for optimal three-and four-dimensional lattice rules of speciied trigonometric degree are discussed. The theory is presented in a general frame emphasising the special nature of lattice rules among the rules of speciied trigonometric degree. 1 Background Material In this paper we discuss some of the results of a recent comput...

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker-Cusa-Huygens type.

In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...