We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel expansion. These polynomials converge to the conformal mapping uniformly on the closure of any Smirnov domain. We prove estimates for the rate of such convergence on domains with piecewise analytic boundaries, expressed...

A class of approximation.s {,5'N,M } to a periodic function f which uses tile ideas of Pad6, or rational function, approximations based on the Fourier series representation of f, rather than oil the Taylor series representation of f, is introduced and studied. Each approximation ,q'X,M is the quotient of a trigonometric polynomial of degree N and a trigonometric polynomial of degree M. The coef...

Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest journal news and information on: • reading the latest articles, free! • receiving free e-mail alerts • submitting your work to EPL Abstract – Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to s...