Abstract. The convergence of a Fourier series on an interval can be interpreted naturally as the convergence of a Laurent series on the unit circle in the complex plane. In turn this Laurent series can be interpreted as the sum of an analytic and a co-analytic Taylor series.The Gibbs phenomenon in this context can be seen as an attempt to approximate a logarithmic branch cut with such series. C...

A two point Padé approximation of the current and quantity of penetrant at the material transport boundary problems in finite membranes is derived from infinite series expansion. These are shown to be in excellent agreement with previous studies

Combinatorial identities that were needed in [24] are proved, mostly with C. Schneider’s computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary order is stated as a conjecture.

Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if th...