What an odd sum!! @drpeyam

Uploaded April 2025 | Updated September 2026, 1 week ago

What an odd sum!!

We use Parseval Theorem to find the sum of reciprocals of odd fourth powers, that is 1 + 1/3^4 + 1/5^4 + ... or in other words the sum of 1/(2n+1)^4 as n ranges from 0 to infinity. For this, we first derive Parseval Formula to the expansion of x as sin(2m+1/2 x) and then find the Fourier coefficients of x with that series. This is a must see for any calculus and partial differential equation lovers, enjoy!

Parseval formula: youtu.be/4DcGpklwP1c
Fourier sine example: youtu.be/_Wtuek3oiGc

Fourier series playlist:
youtube.com/playlist?list=PLJb1qAQIrmmCH7I01p-8p3z2CIenW6hwe

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