Introduction : Quite recently Chebyshev rational approximation to certain entire functions on the whole positive axis has attracted the attention of many mathematicians. In this respect the papers ([3-7, 9]) are worth mentioning. All these papers have been devoted only to entire functions of finite order. On the other hand, methods developed and used in these papers are valid only to entire fun...

The mathematical theory of closed form functions for calculating LSFs on the basis of generating functions is presented. Exploiting recurrence relationships in the series expansion of Chebyshev polynomials of the first kind makes it possible to bootstrap iterative LSF-search from a set of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symme...

We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...

A new class of time-integrators is presented for strongly nonlinear dynamical systems. These algorithms are far superior to the currently common time integrators in computational efficiency and accuracy. These three algorithms are based on a local variational iteration method applied over a finite interval of time. By using Chebyshev polynomials as trial functions andDirac–Delta functions as th...

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...

Kasana and Kumar [5] obtained the (p, q)−growth parameters in terms of Chebyshev and interpolation errors for entire functions on a compact set E of positive transfinite diameter. Rizvi and Nautiyal [9] studied the order and type in terms of these errors for the functions which are not entire. But these results do not give any specific information about the growth of non-entire functions if max...

A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

We give the necessary and su cient conditions guaranteeing the validity of Chebyshev type inequalities for generalized Sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions. For several choices of operators, we characterize the classes of functions for which the Chebyshev type inequality for the classical Sugeno integral is satis ed.

In this paper we characterize rational Szegő quadrature formulas associated with Chebyshev weight functions, by giving explicit expressions for the corresponding para-orthogonal rational functions and weights in the quadratures. As an application, we give characterizations for Szegő quadrature formulas associated with rational modifications of Chebyshev weight functions. Some numerical experime...

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Cheby...