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Results tagged with sequences-and-series
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user 145342
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
3
votes
Express $\int_0^{\pi/2}\{ \operatorname{gd}^{-1}(x)\}dx$ as series of special functions, wit...
$$I=\int_0^{\pi/2}\{ \operatorname{gd}^{-1}(x)\}dx=\int_0^{\frac{\pi}{2}} \frac{\frac{\pi} {2} - x}{\cos x} dx\overset{\frac{\pi} {2} - x=t} =\int_{0}^\frac{\pi}{2}\frac{t}{\sin t}dt$$
$$\overset{IBP} …
- 225
5
votes
How to prove the identity $L(2,(\frac{\cdot}3))=\frac2{15}\sum\limits_{k=1}^\infty\frac{48^k...
To provide an alternative approach, I'll cross-post my answer from MSE, adapted for the series.
Similarly to what @Nemo obtained in the comments, we can transform the original series into an equivalen …
- 225