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convergence of $\sum_n\left(1+\log\left(1+\frac1n\right)\right)^{n^2}x^n$

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#sequences-and-series #limits #power-series #uniform-convergence
152
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Visualizing where uniform convergence fails but pointwise convergence holds

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#real-analysis #uniform-convergence #pointwise-convergence
96
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Rudin Real and Complex analysis exercise 10.20

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#complex-analysis #uniform-convergence
46
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Is it possible that $f_n$ converge uniformly on compact sets?

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#real-analysis #convergence-divergence #continuity #uniform-convergence
128
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Show that the solution to PDE converges to the initial condition in $L^2$

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#sequences-and-series #partial-differential-equations #fourier-series #uniform-convergence #heat-equation
60
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Show uniform convergent of sequence of function given conditions

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#analysis #convergence-divergence #uniform-convergence
45
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Uniform convergence of the PDF in central limit theorem for time-integral of continuous stochastic processes

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#probability #stochastic-processes #stochastic-calculus #uniform-convergence #central-limit-theorem
86
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Dense Set of Functions

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#uniform-convergence #function-spaces #dense-subspaces
249
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Does uniform convergence imply Hölder convergence?

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#real-analysis #functional-analysis #banach-spaces #uniform-convergence #holder-spaces
28
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Uniform convergence of $(t+ix)^{-\beta}$

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#real-analysis #complex-numbers #uniform-convergence
99
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Uniform convergence of functions with values in a Hilbert space

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#hilbert-spaces #uniform-convergence #weak-convergence #strong-convergence
88
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Undergraduate Real Analysis problem books that do not require Topology

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#soft-question #uniform-convergence #book-recommendation #riemann-integration #uniform-continuity
26
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limit of convergence of continuous functions

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#real-analysis #calculus #functional-analysis #uniform-convergence
40
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Evaluate $s(x)$ for $0<x<1$. $ s(x)=\sum_{j=1}^{\infty} \frac{x^j+(1-x)^j}{j^2} . $

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#fourier-series #uniform-convergence
72
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$f_{n}(x)=(x+\frac{1}{n})^2$, $x\in \mathbb{R}$, converges pointwise to $f(x)=x^2$

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#real-analysis #analysis #solution-verification #uniform-convergence

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