Question

Given $P_n(x)=\frac{n}{1+n^2x^2},$ Prove $f_n(x)=\frac{1}{\pi}\int_{-\infty}^\infty f(x-t)P_n(t)$ converges uniformly

score 194 · Answer 1 · 2026-04-17 11:13:59

194

Views

Given $P_n(x)=\frac{n}{1+n^2x^2},$ Prove $f_n(x)=\frac{1}{\pi}\int_{-\infty}^\infty f(x-t)P_n(t)$ converges uniformly

Published on 17 Apr 2026 - 11:13

score 103 · Answer 2 · 2026-04-15 13:40:48

103

Views

Finding a Closed Form for $\int_0^\infty A\sin(\frac{2\pi}{T}x) \exp(-bx)dx$

Published on 15 Apr 2026 - 13:40

score 1.6k · Answer 3 · 2026-04-17 03:25:27

1.6k

Views

Is it true that if $\int_{1}^\infty f(x)dx$ converges, then $\lim_{x\to\infty}f(x)=0$?

Published on 17 Apr 2026 - 3:25

score 269 · Answer 4 · 2026-04-12 03:19:55

269

Views

Investigate convergence of improper integral involving logarithm multiplied by arcsin

Published on 12 Apr 2026 - 3:19

score 63 · Answer 5 · 2026-04-14 23:24:52

63

Views

Compute $\int\limits_{-\infty}^\infty \dfrac{|x|^a}{(1+x^2)^b}dx$

Published on 14 Apr 2026 - 23:24

score 1.1k · Answer 6 · 2026-04-12 07:46:42

1.1k

Views

Does Absolute Improper Integrability imply Lebesgue Integrability?

Published on 12 Apr 2026 - 7:46

score 313 · Answer 7 · 2026-04-14 20:32:47

313

Views

Uniform Convergence of Improper Integral.

Published on 14 Apr 2026 - 20:32

score 82 · Answer 8 · 2026-04-15 01:14:38

82

Views

On the evaluation of a limit of a definite integral

Published on 15 Apr 2026 - 1:14

score 261 · Answer 9 · 2026-04-14 05:24:55

261

Views

"Uniform Convergence" of the integral of a function

Published on 14 Apr 2026 - 5:24

score 768 · Answer 10 · 2026-04-16 23:23:46

768

Views

Evaluate the integral $\int_{\pi/4}^{3\pi/4} x \cdot \cot(x) \cdot \csc(x) \mathop{dx}$

Published on 16 Apr 2026 - 23:23

score 1.2k · Answer 11 · 2026-05-05 01:17:14

1.2k

Views

Term by term integration fourier series

Published on 05 May 2026 - 1:17

score 572 · Answer 12 · 2026-04-11 07:14:49

572

Views

Domain of an integral function

Published on 11 Apr 2026 - 7:14

score 2.3k · Answer 13 · 2026-04-15 13:35:53

2.3k

Views

Infinite area under curve without using derivatives and integrals

Published on 15 Apr 2026 - 13:35

score 4.1k · Answer 14 · 2026-04-17 12:53:38

4.1k

Views

Improper Integral I can't solve $ (1+\sin x)/x^2$

Published on 17 Apr 2026 - 12:53

score 114 · Answer 15 · 2026-04-13 01:32:04

114

Views

Second Integral of Modified Bessel function $ k_o(z)$

Published on 13 Apr 2026 - 1:32

List Question

Given $P_n(x)=\frac{n}{1+n^2x^2},$ Prove $f_n(x)=\frac{1}{\pi}\int_{-\infty}^\infty f(x-t)P_n(t)$ converges uniformly

Finding a Closed Form for $\int_0^\infty A\sin(\frac{2\pi}{T}x) \exp(-bx)dx$

Is it true that if $\int_{1}^\infty f(x)dx$ converges, then $\lim_{x\to\infty}f(x)=0$?

Investigate convergence of improper integral involving logarithm multiplied by arcsin

Compute $\int\limits_{-\infty}^\infty \dfrac{|x|^a}{(1+x^2)^b}dx$

Does Absolute Improper Integrability imply Lebesgue Integrability?

Uniform Convergence of Improper Integral.

On the evaluation of a limit of a definite integral

"Uniform Convergence" of the integral of a function

Evaluate the integral $\int_{\pi/4}^{3\pi/4} x \cdot \cot(x) \cdot \csc(x) \mathop{dx}$

Term by term integration fourier series

Domain of an integral function

Infinite area under curve without using derivatives and integrals

Improper Integral I can't solve $ (1+\sin x)/x^2$

Second Integral of Modified Bessel function $ k_o(z)$

Trending Questions

Popular # Hahtags

Popular Questions