Uniform Approximations for Transcendental Functions

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

Numerical Evaluation of Special Functions

Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. March 1994 December 200

Method of self-similar factor approximants

The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for transcendental functions. In some cases, just a few terms in a power series make it possible to reconstruct a transcendental function exactly. Numerical conver...

On Simultaneous Rational Approximations to a Real Number, Its Square, and Its Cube

We show that, for any transcendental real number ξ, the uniform exponent of simultaneous approximation of the triple (ξ, ξ, ξ) by rational numbers with the same denominator is at most (1 + 2γ − √ 1 + 4γ)/2 ∼= 0.4245 where γ = (1 + √ 5)/2 stands for the golden ratio. As a consequence, we get a lower bound on the exponent of approximation of such a number ξ by algebraic integers of degree at most 4.

Triangular approximations of fuzzy number with value and ambiguity functions