List questions from sequence-of-function

Published on 15 Jan 2022 - 20:03

139

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Example of sequence of functions with counting measure.

Published on 15 Jan 2022 - 23:53

51

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Uniform Cauchy sequence in Bloch space $\mathcal{B}$

Published on 19 Jan 2022 - 16:02

63

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Prove that $\lim\limits_{x\to\infty}g(x)=a$ iff $f_n(x)=g(x+n)$ converges uniformly to $f(x)=a$.

Published on 21 Jan 2022 - 15:45

83

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Comparing different kinds of convergence

Published on 26 Feb 2026 - 7:55

38

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Left side derivative

Published on 23 Jan 2022 - 19:16

35

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Uniform convergence of the sequence, $f_n:[a \geq 0,\infty) \to \mathbb R$ defined by $f_n(x)=\frac{n^2x}{1+n^3x^2},~n \in \mathbb N,$

Published on 25 Jan 2022 - 6:21

73

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Sum of inverse functions

Published on 28 Jan 2022 - 4:40

74

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Give an example of a sequence of functions $f_n$ which is uniformly convergent on $(-1,1)$ and for which $\{f'_n(0)\}$ is unbounded.

Published on 28 Jan 2022 - 19:55

565

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Uniform convergence of $f_n(x)=nx^n(1-x^n)$ on $[0,1]$

Published on 01 Feb 2022 - 4:08

108

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Existence of closed form formulas for integer sequences

Published on 01 Feb 2022 - 6:50

120

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Riemann integral of product of sequence of function with a continuous function at a point.

Published on 07 Feb 2022 - 19:14

44

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Showing that this particular sequence of functions defined by recursion is point-wise bounded

Published on 07 Feb 2022 - 23:40

48

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Calculate $\lim_{n\to\infty} \frac{n\sin(x/n)}{x(x^2+1)}$ in $\mathbb{R}^+$

Published on 08 Feb 2022 - 14:30

33

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Convergence of Sequence of functions with nested radicals.

Published on 09 Feb 2022 - 22:55

List Question

Weak convergence and convergence in measure

Example of sequence of functions with counting measure.

Uniform Cauchy sequence in Bloch space $\mathcal{B}$

Prove that $\lim\limits_{x\to\infty}g(x)=a$ iff $f_n(x)=g(x+n)$ converges uniformly to $f(x)=a$.

Comparing different kinds of convergence

Left side derivative

Uniform convergence of the sequence, $f_n:[a \geq 0,\infty) \to \mathbb R$ defined by $f_n(x)=\frac{n^2x}{1+n^3x^2},~n \in \mathbb N,$

Sum of inverse functions

Give an example of a sequence of functions $f_n$ which is uniformly convergent on $(-1,1)$ and for which $\{f'_n(0)\}$ is unbounded.

Uniform convergence of $f_n(x)=nx^n(1-x^n)$ on $[0,1]$

Existence of closed form formulas for integer sequences

Riemann integral of product of sequence of function with a continuous function at a point.

Showing that this particular sequence of functions defined by recursion is point-wise bounded

Calculate $\lim_{n\to\infty} \frac{n\sin(x/n)}{x(x^2+1)}$ in $\mathbb{R}^+$

Convergence of Sequence of functions with nested radicals.

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