Question

Branch cuts: what makes the use of the Log-Gamma function favourable over the use of the logarithm in contour integration?

score 120 · Answer 1 · 2021-12-07 18:50:48

120

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Branch cuts: what makes the use of the Log-Gamma function favourable over the use of the logarithm in contour integration?

Published on 07 Dec 2021 - 18:50

score 521 · Answer 2 · 2021-12-08 17:37:48

521

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Show that $ \int_{-1}^{1} z^{i} dz= \frac{1 + e^{- \pi}}{2} (1 -i)$

Published on 08 Dec 2021 - 17:37

score 125 · Answer 3 · 2021-12-10 14:06:06

125

Views

Square root branch selection of a polynomial

Published on 10 Dec 2021 - 14:06

score 113 · Answer 4 · 2021-12-19 10:48:37

113

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Square root of continuous function on simply connected domain

Published on 19 Dec 2021 - 10:48

score 108 · Answer 5 · 2022-01-09 15:27:36

108

Views

Deducing $\int_0^{\pi}\log \sin x dx =-\pi\log 2$ from $\int_0^{\pi}\log (-2ie^{ix}\sin x) dx = 0$

Published on 09 Jan 2022 - 15:27

score 42 · Answer 6 · 2022-01-17 09:01:33

42

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Branch cut contour integral - contour understanding

Published on 17 Jan 2022 - 9:01

score 61 · Answer 7 · 2022-01-31 21:21:15

61

Views

How to improve the solution on this problem of branch cut

Published on 31 Jan 2022 - 21:21

score 188 · Answer 8 · 2026-03-26 14:22:46

188

Views

Confusion about the change of variable $z \to \frac{1}{z}$ for a multivalued function

Published on 26 Mar 2026 - 14:22

score 169 · Answer 9 · 2022-02-09 23:53:14

169

Views

Finding branch cuts

Published on 09 Feb 2022 - 23:53

score 68 · Answer 10 · 2026-03-26 04:37:57

68

Views

How to find branch cuts and branch points of $\sqrt(z^a +1)$

Published on 26 Mar 2026 - 4:37

score 118 · Answer 11 · 2022-02-17 11:26:27

118

Views

Difficulty evaluating $\sum_{n=1}^\infty\frac{1}{n^2}\sqrt{\alpha n-1}$ for a real $\alpha\gt1$

Published on 17 Feb 2022 - 11:26

score 43 · Answer 12 · 2026-03-26 14:22:51

43

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How to find a branch which is analytic on the exterior of the unit circle for $\sqrt(z^2 +1)$, $|z| > 1$

Published on 26 Mar 2026 - 14:22

score 84 · Answer 13 · 2022-02-27 19:05:33

84

Views

Which branch of the square root allows $(z^2)^{1/2} = z$

Published on 27 Feb 2022 - 19:05

score 111 · Answer 14 · 2022-03-03 17:37:13

111

Views

$z/\sqrt{-z^2}=-i$ when $\operatorname{arg}(z)\leq 0$?

Published on 03 Mar 2022 - 17:37

score 215 · Answer 15 · 2026-03-26 04:38:06

215

Views

Determine a branch of $f(z)=\log(2iz−z^2)$

Published on 26 Mar 2026 - 4:38

List Question

Branch cuts: what makes the use of the Log-Gamma function favourable over the use of the logarithm in contour integration?

Show that $ \int_{-1}^{1} z^{i} dz= \frac{1 + e^{- \pi}}{2} (1 -i)$

Square root branch selection of a polynomial

Square root of continuous function on simply connected domain

Deducing $\int_0^{\pi}\log \sin x dx =-\pi\log 2$ from $\int_0^{\pi}\log (-2ie^{ix}\sin x) dx = 0$

Branch cut contour integral - contour understanding

How to improve the solution on this problem of branch cut

Confusion about the change of variable $z \to \frac{1}{z}$ for a multivalued function

Finding branch cuts

How to find branch cuts and branch points of $\sqrt(z^a +1)$

Difficulty evaluating $\sum_{n=1}^\infty\frac{1}{n^2}\sqrt{\alpha n-1}$ for a real $\alpha\gt1$

How to find a branch which is analytic on the exterior of the unit circle for $\sqrt(z^2 +1)$, $|z| > 1$

Which branch of the square root allows $(z^2)^{1/2} = z$

$z/\sqrt{-z^2}=-i$ when $\operatorname{arg}(z)\leq 0$?

Determine a branch of $f(z)=\log(2iz−z^2)$

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