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Table 2 Degree of convergence of \(f(t)= \sum_{\nu =2}^{\infty} \frac{\sin \nu t}{\log \nu}\)

From: Degree of convergence of the functions of trigonometric series in Sobolev spaces and its applications

ν \(\tilde{T}_{\nu}(t)= ( \sum_{\nu =2}^{\infty}\frac{1}{\log \nu} ) [\frac{1+\log \pi (\nu +1)}{\nu +1}+\frac{ (\frac{1}{\pi}-(\nu +1) ) (\frac{1}{\pi ^{2}}-(\nu +1)^{2} )}{ (\nu +1)^{2}}] \)
100 −0.15357
1000 −0.15841
10,000 −0.15906
50,000 −0.15913
75,000 −0.15914
100,000 −0.15914
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