Question

$ \int_0^\infty (1+t^2)^{-s} (1+it)^{s'} 2t \; d t.$

score 210 · Answer 1 · 2014-07-09 12:48:59

210

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$ \int_0^\infty (1+t^2)^{-s} (1+it)^{s'} 2t \; d t.$

Published on 09 Jul 2014 - 12:48

score 725 · Answer 2 · 2026-03-27 20:12:15

725

Views

Finding a dominating function for this sequence of functions

Published on 27 Mar 2026 - 20:12

score 70 · Answer 3 · 2026-04-03 03:41:26

70

Views

Show that $\lim_{s \to \infty}F_s(t) = F(t)$ uniformly for $t \in (0,+\infty)$

Published on 03 Apr 2026 - 3:41

score 244 · Answer 4 · 2014-07-10 10:09:05

244

Views

Help finishing this exercise!

Published on 10 Jul 2014 - 10:09

score 2.8k · Answer 5 · 2014-07-10 21:35:06

2.8k

Views

Convergence of an improper integral $\int_0^\infty \frac {1-e^{-x}} {\sqrt x^3}dx$

Published on 10 Jul 2014 - 21:35

score 136 · Answer 6 · 2014-07-10 23:25:32

136

Views

a complicated question about double improper integral

Published on 10 Jul 2014 - 23:25

score 566 · Answer 7 · 2014-07-11 03:05:53

566

Views

How to evaluate integral $\int_{0}^{\infty} \left(\frac{1-e^{-x}}{x}\right)^n dx$.

Published on 11 Jul 2014 - 3:05

score 417 · Answer 8 · 2014-07-11 21:15:29

417

Views

Show $\iint xye^{-xy}\,dx\,dy$ is convergent or divergent

Published on 11 Jul 2014 - 21:15

score 2.2k · Answer 9 · 2014-07-12 20:40:11

2.2k

Views

How to identify continuity or discontinuity of an [Definite] integral?

Published on 12 Jul 2014 - 20:40

score 57 · Answer 10 · 2014-07-13 12:43:38

57

Views

Question on integral

Published on 13 Jul 2014 - 12:43

score 167 · Answer 11 · 2014-07-13 14:50:14

167

Views

Growth restriction for nonnegative, continuous functions whose integrals on $\mathbb{R}$ are bounded

Published on 13 Jul 2014 - 14:50

score 337 · Answer 12 · 2014-07-14 15:56:19

337

Views

Find $\lambda$ if $\int^{\infty}_0 \frac{\log(1+x^2)}{(1+x^2)}dx = \lambda \int^1_0 \frac{\log(1+x)}{(1+x^2)}dx$

Published on 14 Jul 2014 - 15:56

score 287 · Answer 13 · 2026-03-26 09:39:05

287

Views

Parameter-dependent integral: Is the following statement true?

Published on 26 Mar 2026 - 9:39

score 1.5k · Answer 14 · 2014-07-15 06:33:19

1.5k

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Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$

Published on 15 Jul 2014 - 6:33

score 75 · Answer 15 · 2026-03-27 12:20:08

75

Views

Approximate improper Bessel integral

Published on 27 Mar 2026 - 12:20

List Question

$ \int_0^\infty (1+t^2)^{-s} (1+it)^{s'} 2t \; d t.$

Finding a dominating function for this sequence of functions

Show that $\lim_{s \to \infty}F_s(t) = F(t)$ uniformly for $t \in (0,+\infty)$

Help finishing this exercise!

Convergence of an improper integral $\int_0^\infty \frac {1-e^{-x}} {\sqrt x^3}dx$

a complicated question about double improper integral

How to evaluate integral $\int_{0}^{\infty} \left(\frac{1-e^{-x}}{x}\right)^n dx$.

Show $\iint xye^{-xy}\,dx\,dy$ is convergent or divergent

How to identify continuity or discontinuity of an [Definite] integral?

Question on integral

Growth restriction for nonnegative, continuous functions whose integrals on $\mathbb{R}$ are bounded

Find $\lambda$ if $\int^{\infty}_0 \frac{\log(1+x^2)}{(1+x^2)}dx = \lambda \int^1_0 \frac{\log(1+x)}{(1+x^2)}dx$

Parameter-dependent integral: Is the following statement true?

Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$

Approximate improper Bessel integral

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