We study integer sequences and transforms that operate on them. Many of these transforms are defined by triangular arrays of integers, with a particular focus on Riordan arrays and Pascal-like arrays. In order to explore the structure of these transforms, use is made of methods coming from the theory of continued fractions, hypergeometric functions, orthogonal polynomials and most importantly f...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

A simple strategy for constructing a sequence of increasingly refined interpolation grids over the triangle or the tetrahedron is discussed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The interpolation nodes are generated based on a one-dimensional master grid comprised of the zeros of the Lobatto, Legendre, Chebyshev, and second-kind Chebyshev polyn...

We study the regularity of form ( linear functional) satisfying functional equation (x2 ? c2)u = ?v where c C, C {0} and v is perturbed order one Chebyshev second kind. The integral representation u highlighted. Moreover, some symmetric degree forms class two four are given.

with given a, b, t0, t1 and n ≥ 0. This sequence was introduced by Horadam [3] in 1965, and it generalizes many sequences (see [1, 4]). Examples of such sequences are Fibonacci polynomials sequence (Fn(x))n≥0, Lucas polynomials sequence (Ln(x))n≥0, and Pell polynomials sequence (Pn(x))n≥0, when one has a = x, b = t1 = 1, t0 = 0; a = t1 = x, b = 1, t0 = 2; and a = 2x, b = t1 = 1, t0 = 0; respect...

In this work a study of efficient approximate methods for solving the Cauchy type singular integral equations (CSIEs) of the first kind, over a finite interval, is presented. In the solution, Chebyshev polynomials of the first kind, Tn(x)Tn(x), second kind, Un(x)Un(x), third kind, Vn(x)Vn(x), and fourth kind, Wn(x)Wn(x), corresponding to respective weight functions View the MathML sourceW(1)(x)...

We say that a monic polynomial with integer coefficients is polygomial if its each zero obtained by squaring the edge or diagonal of regular n-gon unit circumradius. find connections certain polygomials Morgan-Voyce polynomials and further Chebyshev second kind.