Question

Find the analytic continuation of the $ f(z) = \int_{0}^{\infty} \frac{exp(-zt)}{1+t^2} dt$

score 528 · Answer 1 · 2026-04-16 16:25:38

528

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Find the analytic continuation of the $ f(z) = \int_{0}^{\infty} \frac{exp(-zt)}{1+t^2} dt$

Published on 16 Apr 2026 - 16:25

score 68 · Answer 2 · 2026-04-16 22:36:06

68

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Computing $\int_0^{2\pi}(1+2\cos t)^n\cos nt\ \mathrm{d}t$

Published on 16 Apr 2026 - 22:36

score 103 · Answer 3 · 2026-04-14 13:41:49

103

Views

Bromwich integral of $1/s^k$ with k real (non integer) and $1<k$

Published on 14 Apr 2026 - 13:41

score 594 · Answer 4 · 2026-04-12 14:09:33

594

Views

Laplace transform of and impulse sampled function using "frequency" convolution

Published on 12 Apr 2026 - 14:09

score 915 · Answer 5 · 2026-04-12 02:37:55

915

Views

Using residue theorem to solve double integral, involving singular roots?

Published on 12 Apr 2026 - 2:37

score 294 · Answer 6 · 2026-04-14 13:36:26

294

Views

Integral Involving Trigonometric Functions and Exponential (Related to Marcum Q-function)

Published on 14 Apr 2026 - 13:36

score 228 · Answer 7 · 2026-04-17 04:09:34

228

Views

Integral $\int_0^1 \frac{\tanh^{-1}(x)\ln x}{x(1-x^2)} \, dx $

Published on 17 Apr 2026 - 4:09

score 1.2k · Answer 8 · 2026-04-12 05:24:39

1.2k

Views

Integral, definite integral

Published on 12 Apr 2026 - 5:24

score 447 · Answer 9 · 2026-04-16 07:22:02

447

Views

A definite integral involving logarithmic functions: $\int_{0}^{1} \frac{\ln(x) \ln (1+x)}{1-x} \, \mathrm{d} x$

Published on 16 Apr 2026 - 7:22

score 1k · Answer 10 · 2026-04-11 21:56:42

1k

Views

Complex integrals over an ellipse instead of circle?

Published on 11 Apr 2026 - 21:56

score 215 · Answer 11 · 2026-04-12 09:09:19

215

Views

Find the residue(s) of this function at each pole that lies in the contour?

Published on 12 Apr 2026 - 9:09

score 124 · Answer 12 · 2026-04-13 01:40:02

124

Views

definiteinteggral

Published on 13 Apr 2026 - 1:40

score 64 · Answer 13 · 2026-04-14 21:39:49

64

Views

Cauchy Riemann equations, do these satisfy it??

Published on 14 Apr 2026 - 21:39

score 335 · Answer 14 · 2026-04-16 20:43:40

335

Views

Computing the integral $ \int_0^{\infty} e^{-\phi^2+\phi}\cdot \phi^{2} \ln(1-2x\cos\phi+x^2)\, d\phi. $

Published on 16 Apr 2026 - 20:43

score 1.3k · Answer 15 · 2026-04-16 15:24:22

1.3k

Views

Why does the Cauchy-Goursat theorem not apply here?

Published on 16 Apr 2026 - 15:24

List Question

Find the analytic continuation of the $ f(z) = \int_{0}^{\infty} \frac{exp(-zt)}{1+t^2} dt$

Computing $\int_0^{2\pi}(1+2\cos t)^n\cos nt\ \mathrm{d}t$

Bromwich integral of $1/s^k$ with k real (non integer) and $1<k$

Laplace transform of and impulse sampled function using "frequency" convolution

Using residue theorem to solve double integral, involving singular roots?

Integral Involving Trigonometric Functions and Exponential (Related to Marcum Q-function)

Integral $\int_0^1 \frac{\tanh^{-1}(x)\ln x}{x(1-x^2)} \, dx $

Integral, definite integral

A definite integral involving logarithmic functions: $\int_{0}^{1} \frac{\ln(x) \ln (1+x)}{1-x} \, \mathrm{d} x$

Complex integrals over an ellipse instead of circle?

Find the residue(s) of this function at each pole that lies in the contour?

definiteinteggral

Cauchy Riemann equations, do these satisfy it??

Computing the integral $ \int_0^{\infty} e^{-\phi^2+\phi}\cdot \phi^{2} \ln(1-2x\cos\phi+x^2)\, d\phi. $

Why does the Cauchy-Goursat theorem not apply here?

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