New posts in Residue Calculus

Show that $\text{Res}_{z = \infty}\left(f(z)\log\left(\frac{z-a}{z-b}\right)\right) = - \int_{a}^{b}f(z)\,dz$

Calculate the value of $\int_0^\infty \frac{\sqrt{x}\cos(\ln(x))}{x^2+1}\,dx$

Evaluating complex integral $\int_{0}^{\pi} \frac {x \sin x}{1+a^2-2a(\cos x)} $ via different contour

Prove that $\int\limits_{-\infty}^{\infty} \frac{e^{-x}}{1+e^{-2\pi x}}\,dx=\frac1{2\sin\left(\frac{1}{2}\right)}$

how to calculate the value of $\int_{-\infty}^\infty \frac{e^{ax}}{\cosh x}\,dx$

Integration of $\int_{-1}^{1}\frac{dx}{(x-a)\sqrt{1-x^2}}$ using Residue Calculus

A Ramanujan sum involving $\sinh$

On twisted Euler sums

Evaluate $\sum_{n=1}^\infty\frac{\sin(n)}{n^3}$

Inverse Laplace Transform of $e^{-\sqrt{s^2+s}}$.