List questions from contour-integration

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414

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Integral using Cauchy's integral formula and residue theorem

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Is there a deep reason why replacing $\cos(x)$ with $e^{ix}$ and taking the real part often makes a contour integral work out?

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631

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Definite integral $1/(x^2-b^2)$ over the real axis

Published on 06 Aug 2015 - 8:28

97

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Solve the following contour integral (Complex Analysis)

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434

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Integrate $\int_{-\infty}^{\infty} \frac{\cosh(\beta x)}{1+\cosh( \beta x )} e^{-x^2} x^2 \rm{d}x$

Published on 07 Aug 2015 - 15:22

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What is a "Contour Integral" and how do I evaluate one?

Published on 11 Apr 2026 - 13:59

853

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Branch cuts for the contour integral $\int_{-1}^{1} \frac{\ln(x+a)}{(x+b) \, \sqrt{1-x^{2}}} \, dx$

Published on 11 Aug 2015 - 18:57

222

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Question about Meijer-G definition and identity

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381

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Problem withlimits on Line Integral

Published on 17 Aug 2015 - 7:53

78

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Evaluating the integral $\int_{-\infty}^{\infty}{e^{2i\mu t}\frac{{\sin^2{\lambda t}}}{\lambda t^2}}dt$

Published on 01 Apr 2026 - 14:54

410

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Evaluate $\int_0^\infty \frac{\sqrt{x}}{x^2+1}\log\left(\frac{x+1}{2\sqrt{x}}\right)\;dx$

Published on 20 Aug 2015 - 17:00

606

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Contour integral mystery: why is the answer different from Maple/Matlab?

Published on 10 Apr 2026 - 9:55

161

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Generalization to this integral

Published on 22 Aug 2015 - 13:12

234

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Integration of a analytic function

Published on 09 Apr 2026 - 15:56

List Question

Why is $\zeta(1+it) \neq 0$ equivalent to the prime number theorem?

Integral using Cauchy's integral formula and residue theorem

Is there a deep reason why replacing $\cos(x)$ with $e^{ix}$ and taking the real part often makes a contour integral work out?

Definite integral $1/(x^2-b^2)$ over the real axis

Solve the following contour integral (Complex Analysis)

Integrate $\int_{-\infty}^{\infty} \frac{\cosh(\beta x)}{1+\cosh( \beta x )} e^{-x^2} x^2 \rm{d}x$

What is a "Contour Integral" and how do I evaluate one?

Branch cuts for the contour integral $\int_{-1}^{1} \frac{\ln(x+a)}{(x+b) \, \sqrt{1-x^{2}}} \, dx$

Question about Meijer-G definition and identity

Problem withlimits on Line Integral

Evaluating the integral $\int_{-\infty}^{\infty}{e^{2i\mu t}\frac{{\sin^2{\lambda t}}}{\lambda t^2}}dt$

Evaluate $\int_0^\infty \frac{\sqrt{x}}{x^2+1}\log\left(\frac{x+1}{2\sqrt{x}}\right)\;dx$

Contour integral mystery: why is the answer different from Maple/Matlab?

Generalization to this integral

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