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Integrating a fraction of exponential and trignometric using rectangular contour
[Ex 41 ] Watson’s complex integration $$\int^\infty_0 \frac{\sin(ax)}{e^{2\pi x}1}\,dx = \frac{1}{4}\coth\left(\frac{a}{2} \right)\frac{1}{2a}$$ $$\textit{solution}$$ By integrating the following function $$f(z) = \frac{e^{iaz}}{e^{2\pi z}1}$$ The function is analytic in and on the contour, indented at the poles of the function Hence by … Continue reading
Posted in Contour Integration
Tagged analysis, complex, contour, exponent, fraction, rectangle, residue, theorem, trignometric
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