The aim of this paper is to construct generating functions for new families special polynomials including the Appel polynomials, Hermite-Kamp\`e de F\`eriet Milne-Thomson type parametric kinds Apostol numbers and polynomials. Using Euler's formula, relations among functions, Hermite-type Chebyshev Dickson are given. their functional equations, various formulas identities With help computational...

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it possible to derive many infinite integrals, finite integrals integral identities for function represented inverse Laplace transform. The are mainly in terms convolution with Mittag–Leffler Volterra functions. integrands determined include elementary functions (power, exponential, logarithmic, ...

Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this family there is subfamily interpolation-like discovered by Hermite revived rather recently two independent papers, one Wenchang Chu other Warren Johnson exploring various forms generalizations Hermite’s results. The goal work inspired these articles twofold. first fill gap...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

A symmetric basis of trigonometric polynomial space is presented. Based on the basis, symmetric trigonometric polynomial approximants like Bernstein polynomials are constructed. Two kinds of nodes are given to show that the trigonometric polynomial sequence is uniformly convergent. The convergence of the derivative of the trigonometric polynomials is shown. Trigonometric quasi-interpolants of r...

The known proofs of the inverse theorems theory approximation by trigonometric polynomials and functions exponential type are based on idea S. N. Bernstein to expand a function in series containing its best approximation. In this paper, new method establish is introduced. We simple identities that immediately imply mentioned and, moreover, with better constants. This can be applied derivatives ...

We propose the use of finite Fourier series as an alternative means of representing ovals in projective planes of even order. As an example to illustrate the method’s potential, we show that the set {w +w +w : 0 ≤ j ≤ 2} ⊂ GF(2) forms an oval if w is a primitive (2 +1) root of unity in GF(2) and GF(2) is viewed as an affine plane over GF(2). For the verification, we only need some elementary “t...

Lemniscate chaotic map (LCM) provides a wide range of control parameters, canceling the need for several rounds substitutions, and excellent performance in confusion process. Unfortunately, hardware model LCM is complex consumes high power. This paper presents proposed low power called practical lemniscate (P-LCM) depending on trigonometric identities to reduce complexity conventional model. Th...

SUMMARY In this work we consider optimized twiddle factor multipliers based on shift-and-add-multiplication. We propose a low-complexity structure for twiddle factors with a resolution of 32 points. Furthermore, we propose a slightly modified version of a previously reported multiplier for a resolution of 16 points with lower round-off noise. For completeness we also include results on optimal ...