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New posts in residue-calculus
Area integral over complex plane of non-holomorphic gaussian $e^{-z\bar{z}}$
complex-analysis
contour-integration
residue-calculus
complex-integration
Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$
integration
complex-analysis
improper-integrals
contour-integration
residue-calculus
Prove that $\int\limits_{-\infty}^{\infty} \frac{e^{-x}}{1+e^{-2\pi x}}\,dx=\frac1{2\sin\left(\frac{1}{2}\right)}$
integration
complex-analysis
improper-integrals
residue-calculus
complex-integration
Integrating $\int_{-\infty}^\infty \frac{1}{1 + x^4}dx$ with the residue theorem
complex-analysis
residue-calculus
Calculus of residue of function around poles of fractional order (complex analysis)
complex-analysis
residue-calculus
How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
complex-analysis
contour-integration
residue-calculus
Integral by residue - "dog bone"
complex-analysis
contour-integration
residue-calculus
Integral with $\ln$ and rational function
contour-integration
residue-calculus
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
complex-analysis
residue-calculus
$\int_{-\infty}^\infty \frac{\sin (t) \, dt}{t^4+1}$ must be zero and it isn't
complex-analysis
improper-integrals
contour-integration
residue-calculus
Contour Integration $\int_0^1\frac1{\sqrt[n]{1-x^n}}dx$
complex-analysis
contour-integration
residue-calculus
Residue theorem:When a singularity on the circle (not inside the circle)
integration
complex-analysis
contour-integration
residue-calculus
cauchy-principal-value
Computation real integral with residue theorem
complex-analysis
improper-integrals
residue-calculus
Residue theorem with $\frac{1}{2\pi}\int_{0}^{2\pi}e^{\cos\theta}\cos(n\theta) d\theta$.
complex-analysis
contour-integration
residue-calculus
complex-integration
How to show $\int^{\infty}_{-\infty}\frac{\sin(ax)}{x(x^2+1)}dx=\pi(1-e^{-a})$? ($a\ge0$)
complex-analysis
definite-integrals
contour-integration
residue-calculus
Great difficulty in finding the residues of $\frac{\mathrm{Log}\Gamma\left(\frac{z+ai}{2\pi i}\right)}{\cosh(z)+1}$
complex-analysis
limits
gamma-function
residue-calculus
polygamma
Calculate residue at essential singularity
residue-calculus
Applications of the Residue Theorem to the Evaluation of Integrals and Sums
integration
complex-analysis
improper-integrals
contour-integration
residue-calculus
Evaluation by methods of complex analysis $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm{dx}$ [duplicate]
calculus
complex-analysis
residue-calculus
Closed form of an integral involving Lambert function
calculus
integration
closed-form
residue-calculus
lambert-w
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