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 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.

Abstract In this paper we consider the problem of approximation definite integrals on finite intervals for integrand functions showing some kind “pathological” behavior, e.g. “nearly” singular functions, highly oscillating weakly etc. particular, introduce and study a product rule based equally spaced nodes constrained mock-Chebyshev least squares operator. Like other polynomial or rational met...

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...

The Lane-Emden equation has been used to model several phenomenas in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the Rational Chebyshev of Second Kind function (RSC) to solve the Lane-Emden equation over the semi-infinit interval [0,+∞). According to well-known results and com...

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results  to the case of comonotone functions.

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...

In this paper we propose a class of 2D circularly-symmetric filter banks based on a 1D IIR Gaussian prototype. We approach two cases, namely dyadic and uniform filter banks. The Gaussian prototype is obtained using an efficient rational approximation, namely the Chebyshev-Padé approximation. Then, using a frequency transformation, the corresponding 2D filters with circular symmetry are derived....