Questions tagged [contour-integration]

Questions on the evaluation of integrals along a locus in the complex plane.

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Changing Integration Bounds to Compute Contour Integral

So I have an Integral of the form $\int_{0}^{\infty} \frac{f(x)\frac{1 - e^{ibx}}{x} }{E - x^2} dx$ where $f(x)$ is analytic everywhere and goes to zero as $R \to \infty$ for a semicircular contour on ...
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Continuation of the “Lorenzified” Riemann zeta $\zeta_{L}(x)$?

I have been studying a particular function that might be described as, the “Lorenz curve of the Riemann zeta function,” and I am curious about its possible analytic continuation to the complex plane. ...
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How to approach this complex integration problem

Let $\gamma(t)= e^{it}, 0\leq t \leq 6\pi$. Then the value of the integral $$\frac{1}{2\pi i} \int _ {\gamma}\frac{z^{99}}{z^{100}-1}dz$$ equals? We can't use Cauchy integral formula or residue ...
1 vote
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Convergence of integral of gamma function over hankel contour

Let ${H}$ denote hankel contour then I want to show that, $$\oint_{H}t^{z-1}e^{-t}dt$$ Converges for all $z\in\mathbb{C}$. I am familiar that this integral is used in the analytic continuation of ...
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