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Results tagged with limits-and-convergence
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user 500629
Convergence of series, sequences and functions and different modes of convergence.
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Limiting problem for variable being part of derivative of natural degree
I discovered some interesting behaviour of Riemman's functional equation, such assuming Ramanujan's summation;
$$
\begin {split}
\zeta(s) & = 2(2 \pi)^{s-1}\left(\frac{\pi s }{2}\right)\zeta(1-s)\Gamm …
- 161
1
vote
Limiting problem for variable being part of derivative of natural degree
Given formula, for $s \in \mathbb{N}$, $s \geq 2$ should be equal to;
$$ \zeta(s)= \frac{(-2 \pi)^{s-1}}{\Gamma(s)} i\int_{0}^1(1-u)^{-1} u^{s-1} \left[e^{\left(2 \pi u+\frac{\pi s}{2}\right)}Li_{1- …
- 161