Uploaded March 2025 | Updated September 2026, 1 week ago
Sum of 1/n^4
We calculate the famous sum of 1/n^4 = 1/1^4 + 1/2^4 + 1/3^4 + ... This is a really nice application of Parseval's formula, which relates the sums of squares of this time the Fourier cosine coefficients of f. Applying this to f(x) = x^2 gives the sum, which falls out like bread and butter. This is a must-see for anyone who loves partial differential equations or Fourier series.
Parseval formula: youtu.be/4DcGpklwP1c
Fourier cosine example: youtu.be/lM8LgKPvRv0
Fourier series playlist:
youtube.com/playlist?list=PLJb1qAQIrmmCH7I01p-8p3z2CIenW6hwe
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
Sum of 1/n^4
We calculate the famous sum of 1/n^4 = 1/1^4 + 1/2^4 + 1/3^4 + ... This is a really nice application of Parseval's formula, which relates the sums of squares of this time the Fourier cosine coefficients of f. Applying this to f(x) = x^2 gives the sum, which falls out like bread and butter. This is a must-see for anyone who loves partial differential equations or Fourier series.
Parseval formula: youtu.be/4DcGpklwP1c
Fourier cosine example: youtu.be/lM8LgKPvRv0
Fourier series playlist:
youtube.com/playlist?list=PLJb1qAQIrmmCH7I01p-8p3z2CIenW6hwe
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
