Question

Determine the polynomial $P_n(x)=\frac{1}{2^n n!}\frac{d^n}{dx^n}(x^2-1)^n$ by using the binomial theorem.

score 58 · Answer 1 · 2026-04-25 21:31:09

58

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Determine the polynomial $P_n(x)=\frac{1}{2^n n!}\frac{d^n}{dx^n}(x^2-1)^n$ by using the binomial theorem.

Published on 25 Apr 2026 - 21:31

score 372 · Answer 2 · 2026-04-10 19:20:19

372

Views

Squared Dirichlet integral.

Published on 10 Apr 2026 - 19:20

score 50 · Answer 3 · 2026-04-16 10:38:59

If $f$ is continuous on an interval and $g(x) = \sin f(x)$, then does there exist $k \in \mathbb{Z}$ such that $f(x) = (-1)^k\arcsin g(x) + k\pi$?

score 2k · Answer 4 · 2026-05-03 01:16:23

2k

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Finding the limit of a sequence of integrals

Published on 03 May 2026 - 1:16

score 176 · Answer 5 · 2026-04-11 09:29:50

176

Views

Rudin's PMA, theorem 4.20. A continuous function which is not uniformly continuous on a set which is not closed

Published on 11 Apr 2026 - 9:29

score 67 · Answer 6 · 2026-04-09 01:45:55

67

Views

An equality in Fourier analysis

Published on 09 Apr 2026 - 1:45

score 267 · Answer 7 · 2026-04-15 18:07:17

267

Views

Prove that prove that $\sum_{n=1}^{\infty} \frac{\log(1 + \frac{x}{n})}{n}$ is not uniformly convergent on $\mathbb{R}$ by contradiction

Published on 15 Apr 2026 - 18:07

score 213 · Answer 8 · 2026-04-13 00:49:20

213

Views

Limit of functions on a undefined neighborhood

Published on 13 Apr 2026 - 0:49

score 756 · Answer 9 · 2026-04-14 13:30:03

756

Views

Example for continuous function on the metric space R

Published on 14 Apr 2026 - 13:30

score 280 · Answer 10 · 2026-04-16 03:29:13

280

Views

almost uniform convergence and uniform convergence

Published on 16 Apr 2026 - 3:29

score 287 · Answer 11 · 2026-04-29 12:54:58

287

Views

Proving EVT with epsilon-delta

Published on 29 Apr 2026 - 12:54

score 92 · Answer 12 · 2026-04-17 09:29:41

92

Views

Is the sequence uniformly convergent over [0,1]?

Published on 17 Apr 2026 - 9:29

score 309 · Answer 13 · 2026-04-14 00:03:54

309

Views

A strange condition for a function of two variables

Published on 14 Apr 2026 - 0:03

score 390 · Answer 14 · 2026-04-09 00:05:15

390

Views

Confusion about definition of uniformly continuous function

Published on 09 Apr 2026 - 0:05

score 95 · Answer 15 · 2026-04-17 09:54:43

Find a contradiction to: If $t^n < (\sup \{t \in \mathbb{R}_{>0}: t^n < x\})^n$ then $t^n < x$ when this supremum is greater than $x$.

List Question

Determine the polynomial $P_n(x)=\frac{1}{2^n n!}\frac{d^n}{dx^n}(x^2-1)^n$ by using the binomial theorem.

Squared Dirichlet integral.

If $f$ is continuous on an interval and $g(x) = \sin f(x)$, then does there exist $k \in \mathbb{Z}$ such that $f(x) = (-1)^k\arcsin g(x) + k\pi$?

Finding the limit of a sequence of integrals

Rudin's PMA, theorem 4.20. A continuous function which is not uniformly continuous on a set which is not closed

An equality in Fourier analysis

Prove that prove that $\sum_{n=1}^{\infty} \frac{\log(1 + \frac{x}{n})}{n}$ is not uniformly convergent on $\mathbb{R}$ by contradiction

Limit of functions on a undefined neighborhood

Example for continuous function on the metric space R

almost uniform convergence and uniform convergence

Proving EVT with epsilon-delta

Is the sequence uniformly convergent over [0,1]?

A strange condition for a function of two variables

Confusion about definition of uniformly continuous function

Find a contradiction to: If $t^n < (\sup \{t \in \mathbb{R}_{>0}: t^n < x\})^n$ then $t^n < x$ when this supremum is greater than $x$.

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