Geodesic
On the behavior near the origin of double sine series with monotone coefficients
Mathematica Bohemica, Tome 134 (2009) no. 3, pp. 255-273.

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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 $$ g(x,y)\sim mna_{m,n}+\frac mn\sum _{l=1}^{n-1}la_{m,l}+\frac nm\sum _{k=1}^{m-1}ka_{k,n}+\frac 1{mn}\sum _{l=1}^{n-1}\sum _{k=1}^{m-1}kla_{k,l}, $$ where $x\in (\frac {\pi }{m+1}, \frac {\pi }m]$, $ y\in (\frac {\pi }{n+1}, \frac {\pi }n]$, $ m, n=1,2,\dots $.
DOI : 10.21136/MB.2009.140660
Classification : 42A16, 42A20
Keywords: double sine series; sum of a double sine series with monotone coefficients 
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Krasniqi, Xhevat Z. On the behavior near the origin of double sine series with monotone coefficients. Mathematica Bohemica, Tome 134 (2009) no. 3, pp. 255-273. doi : 10.21136/MB.2009.140660. http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140660/

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