We consider the evaluation of a recent generalization of the Epstein-Hubbell elliptic-type integral using the tau method approximation with a Chebyshev polynomial basis. This also leads to an approximation of Lauricella’s hypergeometric function of three variables. Numerical results are given for polynomial approximations of degree 6.

In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [−1, 1] to arbitrary complex poles outside [−1, 1]. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrat...

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

The theorem proved here extends Chebyshev theory into what has previously been no man's land: functions which have an infinite number of bounded derivatives on the expansion interval [a, b] but which are singular at one endpoint. The Chebyshev series in l/x for all the familiar special functions fall into this category, so this class of functions is very important indeed. In words, the theorem ...

We propose a novel method for studying the production of anticentauro events in high energy heavy ion collisions utilizing Chebyshev expansion coefficients. These coefficients have proved to be very efficient in investigating the pattern of fluctuations in neutral pion fraction. For the anticentauro like events, the magnitude of first few coefficients is strongly enhanced (≈3 times) as compared...

We provide an algorithm to compute arbitrarily many nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with complex poles outside [−1, 1]. Contrary to existing rational quadrature formulas, the computational effort is very low, even for extremely high degrees, and under certain conditions on the poles it can be shown that the c...

The problem of crack propagation along the interface of two bonded dissimilar orthotropic plates is considered. Using Galilean transformation, the problem is reduced to a quasistatic one. Then, using Fourier transforms and asymptotic analysis, the problem is reduced to a pair of singular integral equations with Cauchy-type singularity. These equations are solved using Gauss-Chebyshev quadrature...

The matrix D kI in polynomial approximations of order N is similar to a large Jordan block which is invertible for nonzero k but extremely sensitive to perturbation. Solving the problem (D kI)f = g involves similarity transforms whose condition number grows as N !, which exceeds typical machine precision for N > 17. By using orthogonal projections, we reformulate the problem in terms of Q, the ...

For n × n Vandermonde matrix Vn = (αi−1 j )1≤i j≤n with translated Chebyshev zero nodes, it is discovered that V T n admits an explicit QR decomposition with the R-factor consisting of the coefficients of the translated Chebyshev polynomials of degree less than n. This decomposition then leads to an exact expression for the condition number of its submatrix Vk,n = (αi−1 j )1≤i≤k,1≤j≤n (so-calle...