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Interchange of differentiation and summation in infinite sums
Is it possible to interchange differentiation and summation for infinite but also uniformly convergent sums, like:
$\dfrac{d}{dx} \sin{x} = \dfrac{d}{dx}\sum_{n=0}^\infty (-1)^{n} \, \dfrac{x^{2n + 1}}...
- 181
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Convergence of specific power series
I have to evaluate pointwise/uniform/total convergence of this series and I didn't quite understand how to do it.
$$\sum_{k=2}^{+\infty}{\ln k \over 2+\sin k}x^k$$
For pointwise convergence: it ...
- 415