Non-uniform Convergence, and the Integration of Series
نویسندگان
چکیده
منابع مشابه
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.
متن کاملUniform 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 ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1901
ISSN: 0024-6115
DOI: 10.1112/plms/s1-34.1.245