Question

Convergence. Cauchy and uniform

score 95 · Answer 1 · 2020-06-27 14:20:56

95

Views

Convergence. Cauchy and uniform

Published on 27 Jun 2020 - 14:20

score 277 · Answer 2 · 2026-02-24 19:37:37

277

Views

A sequence of functions $f_n : [0, 1] → R$ which converges uniformly to a discontinuous function $f(x)$.

Published on 24 Feb 2026 - 19:37

score 82 · Answer 3 · 2020-06-28 10:11:22

82

Views

Prove the uniform convergence of ${\frac{1}{(1+ {\frac{y^2}{n}})^n}}$

Published on 28 Jun 2020 - 10:11

score 46 · Answer 4 · 2020-06-28 10:55:14

46

Views

Uniform convergence of series of function defined by recurrence formula

Published on 28 Jun 2020 - 10:55

score 55 · Answer 5 · 2020-06-28 10:55:19

55

Views

Why $\sum_{n=1}^{\infty}\frac{x^{\alpha}}{1+n^2 x^2}$ doesn't converge uniformly on $[0, \infty)$ for $\alpha > 2$?

Published on 28 Jun 2020 - 10:55

score 119 · Answer 6 · 2026-02-24 19:35:39

119

Views

Show that $g_n$ converges to $g$ uniformly.

Published on 24 Feb 2026 - 19:35

score 57 · Answer 7 · 2020-06-29 18:49:22

57

Views

Generalization of term by term differentiation theorem for function series

Published on 29 Jun 2020 - 18:49

score 91 · Answer 8 · 2020-07-02 07:20:39

91

Views

Proving that a sequence of hokomorphic functions does not converge uniformly on the unit disk

Published on 02 Jul 2020 - 7:20

score 96 · Answer 9 · 2020-07-05 06:39:35

96

Views

Does there exist the following theorem for complex case?

Published on 05 Jul 2020 - 6:39

score 24 · Answer 10 · 2026-03-25 04:43:31

24

Views

Will $\sqrt{h \sum_{i =0}^{N-1} （1 - u_i^2)^2} < C_1$ imply there exist $C_2$ satisfies $\sqrt{h \sum_{i=0}^{N-1} u_i^2} < C_2$

Published on 25 Mar 2026 - 4:43

score 65 · Answer 11 · 2020-07-08 23:27:05

65

Views

Uniform convergence of $f_n(x) = \frac{x^ne^{-x}}{(2n)!}$

Published on 08 Jul 2020 - 23:27

score 81 · Answer 12 · 2020-07-09 09:41:44

81

Views

I don't understand uniform convergence

Published on 09 Jul 2020 - 9:41

score 139 · Answer 13 · 2020-07-09 15:17:47

139

Views

Show that the sequence $\left\{\frac{1}{1+nz}\right\}$ is uniformly convergent to zero for all $z$ such that $|z|\geq 2$.

Published on 09 Jul 2020 - 15:17

score 1.1k · Answer 14 · 2020-07-09 17:31:36

1.1k

Views

Show that the power series $\sum_{n=0}^\infty \frac{z^n}{n!}$ converges uniformly for all $z$.

Published on 09 Jul 2020 - 17:31

score 57 · Answer 15 · 2020-07-09 19:28:28

57

Views

Can someone explain to me to find the disk of convergence of the Taylor Series $\frac{3}{1+z}$.

Published on 09 Jul 2020 - 19:28

List Question

Convergence. Cauchy and uniform

A sequence of functions $f_n : [0, 1] → R$ which converges uniformly to a discontinuous function $f(x)$.

Prove the uniform convergence of ${\frac{1}{(1+ {\frac{y^2}{n}})^n}}$

Uniform convergence of series of function defined by recurrence formula

Why $\sum_{n=1}^{\infty}\frac{x^{\alpha}}{1+n^2 x^2}$ doesn't converge uniformly on $[0, \infty)$ for $\alpha > 2$?

Show that $g_n$ converges to $g$ uniformly.

Generalization of term by term differentiation theorem for function series

Proving that a sequence of hokomorphic functions does not converge uniformly on the unit disk

Does there exist the following theorem for complex case?

Will $\sqrt{h \sum_{i =0}^{N-1} （1 - u_i^2)^2} < C_1$ imply there exist $C_2$ satisfies $\sqrt{h \sum_{i=0}^{N-1} u_i^2} < C_2$

Uniform convergence of $f_n(x) = \frac{x^ne^{-x}}{(2n)!}$

I don't understand uniform convergence

Show that the sequence $\left\{\frac{1}{1+nz}\right\}$ is uniformly convergent to zero for all $z$ such that $|z|\geq 2$.

Show that the power series $\sum_{n=0}^\infty \frac{z^n}{n!}$ converges uniformly for all $z$.

Can someone explain to me to find the disk of convergence of the Taylor Series $\frac{3}{1+z}$.

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