Uniform convergence criterion for non-harmonic sine series

Uniform convergence of single and double sine series and integrals

Godement’s criterion for convergence of Eisenstein series

The point is a relatively simple presentation of what turns out to be a sharp estimate for the region of convergence of the relatively simple Siegel-type Eisenstein series [1] on classical groups. The argument is essentially due to Godement, reproduced for real Lie groups by Borel in AMS Proc. Symp. Pure Math. IX (The Boulder Conference 1966). The necessary small excursion into reduction theory...

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.

The Convergence of Smarandache Harmonic Series

harmonic series. The article shows that the series I-,lis divergent and n2!2 S-(n) n 1 studies from the numerical point of view the sequence an = I-2-. -In(n). 1=2 S (1)

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 ...