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Results tagged with limits-and-convergence
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user 36688
Convergence of series, sequences and functions and different modes of convergence.
6
votes
Pointwise convergence for continuous functions
There is sequence of continuous functions $f_{n}$ on the unit interval $[0,1]$ which converges to a function $f$ such that $f$ is discontinuous at rational points of $(0,1)$, a dense subset …
- 356
5
votes
2
answers
560
views
Geometry of Level sets of elliptic polynomials in two real variables
Updated:
A polynomial $P(x,y)\in \mathbb{R}[x,y]$ is called an elliptic polynomial if its last homogeneous part does not vanish on $\mathbb{R}^2\setminus\{0\}$.The two answers to this post provide a …
- 356
3
votes
1
answer
262
views
Rate of convergence of the Riemann zeta function and the Euler product formula
We consider the Euler product formula $$\sum_{n=1}^\infty \frac{1}{n^s}=\prod_p \frac{1}{1-p^{-s}}$$
I have two questions about this equality:
1)Does the rate of convergence of each side dep …
- 356