Question

Prove that if $|a| \neq R$ then $\int_{|z|=R} \frac{|dz|}{|z-a||z+a|} < \frac{2 \pi R}{|R^2-|a|^2|}$

score 56 · Answer 1 · 2024-03-08 22:05:12

56

Views

Prove that if $|a| \neq R$ then $\int_{|z|=R} \frac{|dz|}{|z-a||z+a|} < \frac{2 \pi R}{|R^2-|a|^2|}$

Published on 08 Mar 2024 - 22:05

score 36 · Answer 2 · 2026-04-02 11:45:34

36

Views

Verifying Fourier inversion for a rectangular function

Published on 02 Apr 2026 - 11:45

score 145 · Answer 3 · 2026-04-02 11:37:04

145

Views

Can contour integration produce mascheroni or Catalan's constant?

Published on 02 Apr 2026 - 11:37

score 34 · Answer 4 · 2024-03-13 01:40:35

34

Views

If f is holomorphic on and inside a circle, then show that the maximum of |f| must be on the boundary unless f is constant

Published on 13 Mar 2024 - 1:40

score 47 · Answer 5 · 2026-03-27 17:52:33

47

Views

Would the following not be a correct proof of Cauchy's Integral Theorem?

Published on 27 Mar 2026 - 17:52

score 79 · Answer 6 · 2024-03-15 21:23:20

79

Views

Compute $\int_{|z|=1} |z-1| \, |dz|$

Published on 15 Mar 2024 - 21:23

score 95 · Answer 7 · 2024-03-17 22:29:58

95

Views

Contour Integral of $1/z dz$ with triangle

Published on 17 Mar 2024 - 22:29

score 31 · Answer 8 · 2026-04-03 16:00:36

31

Views

(Re-)Parametrization of contour integrals

Published on 03 Apr 2026 - 16:00

score 55 · Answer 9 · 2026-04-02 13:22:26

55

Views

Residue theorem integral - calculating with trigonometric functions

Published on 02 Apr 2026 - 13:22

score 167 · Answer 10 · 2026-04-01 10:45:05

167

Views

Integration of hypergeometric function on complex plane

Published on 01 Apr 2026 - 10:45

score 41 · Answer 11 · 2024-03-21 15:23:59

41

Views

Question About Independence Of Complex Contour Integral Over Homotopic Path.

Published on 21 Mar 2024 - 15:23

score 65 · Answer 12 · 2026-03-27 17:57:43

65

Views

integration of$ f(z)=\frac{1}{z^4+1}$ using Cauchy's Integral Formula vs. Partial Fractions

Published on 27 Mar 2026 - 17:57

score 147 · Answer 13 · 2026-03-26 18:59:50

147

Views

How to evaluate $\int_{-\infty}^\infty \sin^3(x)/x^3 dx$ without finding an analytic continuation, still using complex analysis.

Published on 26 Mar 2026 - 18:59

score 139 · Answer 14 · 2026-04-02 13:23:00

139

Views

$\int_{-\infty}^\infty \frac{1}{x^5+1}dx$ using contour integration.

Published on 02 Apr 2026 - 13:23

score 33 · Answer 15 · 2024-03-27 04:54:53

33

Views

Finding the imaginary part of a contour integral with a double pole

Published on 27 Mar 2024 - 4:54

List Question

Prove that if $|a| \neq R$ then $\int_{|z|=R} \frac{|dz|}{|z-a||z+a|} < \frac{2 \pi R}{|R^2-|a|^2|}$

Verifying Fourier inversion for a rectangular function

Can contour integration produce mascheroni or Catalan's constant?

If f is holomorphic on and inside a circle, then show that the maximum of |f| must be on the boundary unless f is constant

Would the following not be a correct proof of Cauchy's Integral Theorem?

Compute $\int_{|z|=1} |z-1| \, |dz|$

Contour Integral of $1/z dz$ with triangle

(Re-)Parametrization of contour integrals

Residue theorem integral - calculating with trigonometric functions

Integration of hypergeometric function on complex plane

Question About Independence Of Complex Contour Integral Over Homotopic Path.

integration of$ f(z)=\frac{1}{z^4+1}$ using Cauchy's Integral Formula vs. Partial Fractions

How to evaluate $\int_{-\infty}^\infty \sin^3(x)/x^3 dx$ without finding an analytic continuation, still using complex analysis.

$\int_{-\infty}^\infty \frac{1}{x^5+1}dx$ using contour integration.

Finding the imaginary part of a contour integral with a double pole

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