awesome exponential trig double factorial integral @drpeyam

Uploaded October 2024 | Updated September 2026, 1 week ago

awesome integral with a surprising answer

We calculate the integral of exp(2 cos(x)) from 0 to pi using series and complex analysis, more specifically power series and residue calculus. The result is guaranteed to surprise you and is related to Bessel functions in physics. This is a must-see for any complex analysis lover, enjoy!!

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awesome exponential trig double factorial integral

$Fourier Transform Example Fourier Transform Example Fourier transforms are hard!! Which is why it would be nice to have a concrete example of a Fourier transform, which we do precisely in this video. Here we calculate the Fourier transform of the Gaussian function e^-x^2 or exp(-x squared) and the beautiful result is that it is again a Gaussian! This self-similarity or fractal property will be crucial when well solve the heat equation using the Fourier transform What is the Fourier transform: https://youtu.be/o5jovJ4mkwI Subscribe to my channel: https://youtube.com/drpeyam Instagram: https://www.instagram.com/peyamstagram/ Teespring merch: https://dr-peyam.creator-spring.com/?$