On the uniform convergence of double sine series

Uniform convergence of single and double sine series and integrals

Uniform Convergence of Double Trigonometric Series

It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone ...

Uniform convergence of hypergeometric series

The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.

On the Uniform Convergence and L-convergence of Double Fourier Series with Respect to the Walsh–kaczmarz System

In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces C and L. From our results we obtain different criteria of the uniform convergence and L-convergence of a double Fourier–Kaczmarz series. 2000 Mathematics Subject Classification: Primary 41A50; Secondary 42C10.

On Accelerating the Convergence of Infinite Double Series and Integrals

The generalization of Shanks' e-transformation to double series is discussed and a class of nonlinear transformations, the [A/S]f£ transformations, for accelerating the convergence of infinite double series is presented. It is constructed so as to sum exactly infinite double series whose terms satisfy certain finite linear double difference equations; in that sense it is a generalization of Sha...