On surfaces with constant mean curvature

H. Fath el Bab

On the behavior near the origin of double sine series with monotone coefficients

Xhevat Z. Krasniqi (2009)

Mathematica Bohemica

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In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients $a_{k, l}$ satisfy certain conditions) the following order equality is proved $g (x, y) \sim m n a_{m, n} + \frac{m}{n} \sum_{l = 1}^{n - 1} l a_{m, l} + \frac{n}{m} \sum_{k = 1}^{m - 1} k a_{k, n} + \frac{1}{m n} \sum_{l = 1}^{n - 1} \sum_{k = 1}^{m - 1} k l a_{k, l},$ where $x \in (\frac{π}{m + 1}, \frac{π}{m}]$ , $y \in (\frac{π}{n + 1}, \frac{π}{n}]$ , $m, n = 1, 2, \dots$ .

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