Integral of e^(ikx) from -pi to pi where k is an integer,

Complex Fourier Series: https://youtu.be/aC0j8CW58AM

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Fourier Series of e^x from -pi to pi, featuring Sum of (-1)^n/(1+n^2), fourier series engineering mathematics
Fourier Series Formulas: https://youtu.be/iSw2xFhMRN0
Integral of e^(ax)*cos(bx), integral of e^(ax)*sin(bx), https://youtu.be/E_ecLWj_rcM

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We will derive the coefficients formula for the complex Fourier series.
The Real Fourier Series, https://youtu.be/iSw2xFhMRN0
Complex definition of sine and cosine, https://youtu.be/CjQTWtW_x9o
Integral of e^(ikx) from -pi to pi, https://youtu.be/BIfy7vV0LmE…

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In this video, I explicitly calculate the sum of 1/n^2+1 from 0 to infinity. Does the answer involve arctan? Does it involve pi^2/6 ? Watch this video to find out!

To calculate this sum, I use Parseval's identity by finding the Fourier coefficients of e^x.…

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