Uniform Convergence of Fourier–Jacobi Series

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.

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 single and double sine series and integrals

Ultimate Generalization to Monotonicity for Uniform Convergence of Trigonometric Series

Song Ping Zhou , Institute of Mathematics, Zhejiang Sci-Tech University, Xiasha Economic Development Area, Hangzhou, Zhejiang 310018 China, and Department of Mathematics, Statistics & Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 [email protected] Ping Zhou, Dan Sheng Yu 3 Department of Mathematics, Statistics & Computer Science, St. Francis Xavier Univer...

On statistical type convergence in uniform spaces

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.