in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

Under the assumption of existence Stahl's $S$-compact set we give a short proof limit zeros distribution Pade polynomials and convergence in capacity diagonal approximants for generic class algebraic functions. The is direct but not from opposite as original is. means particular that all branch points multi-sheeted Riemann surface function are first order (i.e., assume such square root type). ...

There is increasing interest in q series with jqj = 1. In analysis of these, an important role is played by the behaviour as n!1 of (q; q)n = (1 q)(1 q):::(1 q): We show, for example, that for almost all q on the unit circle log j(q; q)nj = O(logn) i¤ " > 0. Moreover, if q = exp(2 i ) where the continued fraction of has bounded partial quotients, then the above relation is valid with " = 0. Thi...

In this paper, a hybrid technique based on the combining of differential transform approach, Laplace transformation, and Pade approximant is successfully implemented for solving Volterra Integro (VID) equations subject to appropriate conditions. The proposed method known as modified (MDTM) enlarges domain convergence with less computational time. One interesting features algorithm ability produ...

in this work we deal with the question: how can one improve the approximation level for some nonlinear integral equations? good candidates for this aim are semi orthogonal b-spline scaling functions and their duals. although there are different works in this area, only b-spline of degree at most 2 are used for this approximation. here we compute b-spline scaling functions of degree 4 and their ...