Uniform convergence of some trigonometrical 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 in some Limit Theoremsfor Multiple

For n particles diiusing throughout R (or R d), let n;t (A), A 2 B, t 0, be the random measure that counts the number of particles in A at time t. It is shown that for some basic models (Brownian particles with or without branching and diiusion with a simple interaction) the processes f(n;t () ? E n;t ())= p n : t 2 0; M]; 2 C L (R)g, n 2 N, converge in law uniformly in (t;). Previous results c...

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...