Question

Prove $f(x)=\sum_{k=1}^\infty \frac{1}{k!\sqrt{k}}x^k $ defines a continuous function on $\mathbb{R}$.

score 149 · Answer 1 · 2014-06-08 12:06:55

149

Views

Prove $f(x)=\sum_{k=1}^\infty \frac{1}{k!\sqrt{k}}x^k $ defines a continuous function on $\mathbb{R}$.

Published on 08 Jun 2014 - 12:06

score 363 · Answer 2 · 2014-06-08 17:25:46

363

Views

Question on regulated functions

Published on 08 Jun 2014 - 17:25

score 100 · Answer 3 · 2014-06-09 11:02:53

100

Views

If $f_n$ converges uniformly then $\cos(t)f_n$ converges uniformly?

Published on 09 Jun 2014 - 11:02

score 2k · Answer 4 · 2014-06-09 20:20:47

2k

Views

Taylor series of $\sin(x)$ converges uniformly on $[-\pi,\pi]$?

Published on 09 Jun 2014 - 20:20

score 54 · Answer 5 · 2026-03-30 10:44:18

54

Views

Uniform convergence on functions

Published on 30 Mar 2026 - 10:44

score 148 · Answer 6 · 2026-03-26 13:01:02

148

Views

$\int _0^{\pi }\:\sum _{n=0}^{\infty \:}\frac{n\cdot \sin \left(nx\right)}{e^n}dx=\frac{2e}{e^2-1}$

Published on 26 Mar 2026 - 13:01

score 2.2k · Answer 7 · 2014-06-11 17:32:24

2.2k

Views

How to show $\sqrt x$ is uniformly continuous at [0,1] and $[1,\infty )$

Published on 11 Jun 2014 - 17:32

score 99 · Answer 8 · 2014-06-11 20:00:30

99

Views

Which of the following functions on R are uniformly continous?

Published on 11 Jun 2014 - 20:00

score 137 · Answer 9 · 2014-06-12 17:00:39

137

Views

Convergence of tricky series

Published on 12 Jun 2014 - 17:00

score 2.2k · Answer 10 · 2014-06-12 21:22:05

2.2k

Views

Is $f_n(x)=\frac {2nx}{1+n^2x^2}$ uniformly convergent?

Published on 12 Jun 2014 - 21:22

score 267 · Answer 11 · 2014-06-12 22:42:28

267

Views

Uniform convergence and pointwise limit of $f_n(x)=\frac 1{1+x^n}$

Published on 12 Jun 2014 - 22:42

score 510 · Answer 12 · 2014-06-13 13:11:37

510

Views

Uniform convergence of $\sum\limits_{n=1}^\infty \sin \left(\frac{x}{n^2}\right)$

Published on 13 Jun 2014 - 13:11

score 151 · Answer 13 · 2026-03-27 18:27:54

151

Views

How to show that $\sum_{n=1}^\infty (-1)^n\frac {x^2+n}{n^2}$ is uniformly convergent?

Published on 27 Mar 2026 - 18:27

score 63 · Answer 14 · 2014-06-15 12:18:43

63

Views

Find its pointwise limit and determine if its uniform

Published on 15 Jun 2014 - 12:18

score 32 · Answer 15 · 2014-06-15 12:32:26

32

Views

analyticity of an integral

Published on 15 Jun 2014 - 12:32

List Question

Prove $f(x)=\sum_{k=1}^\infty \frac{1}{k!\sqrt{k}}x^k $ defines a continuous function on $\mathbb{R}$.

Question on regulated functions

If $f_n$ converges uniformly then $\cos(t)f_n$ converges uniformly?

Taylor series of $\sin(x)$ converges uniformly on $[-\pi,\pi]$?

Uniform convergence on functions

$\int _0^{\pi }\:\sum _{n=0}^{\infty \:}\frac{n\cdot \sin \left(nx\right)}{e^n}dx=\frac{2e}{e^2-1}$

How to show $\sqrt x$ is uniformly continuous at [0,1] and $[1,\infty )$

Which of the following functions on R are uniformly continous?

Convergence of tricky series

Is $f_n(x)=\frac {2nx}{1+n^2x^2}$ uniformly convergent?

Uniform convergence and pointwise limit of $f_n(x)=\frac 1{1+x^n}$

Uniform convergence of $\sum\limits_{n=1}^\infty \sin \left(\frac{x}{n^2}\right)$

How to show that $\sum_{n=1}^\infty (-1)^n\frac {x^2+n}{n^2}$ is uniformly convergent?

Find its pointwise limit and determine if its uniform

analyticity of an integral

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