Note: Regarding the partial fraction expansion formula for cotangent, there's an alternative proof called the 'Herglotz trick' that doesn't rely on Fourier expansion. Special thanks to the commenter for pointing this out :)
The famous proof of the Basel problem is mathematically correct. However, the proof about the factorization of sin x (infinite product) is often omitted. This video is intended for those who are curious about the omitted proof (although I wonder if there's a demand for such an explanation.) There are multiple proofs for the infinite product expansion of sin x, and I have chosen a method that does not require knowledge of complex functions.
[BGM]
かえるのピアノ
ほのぼのワルツ【リコーダー】(commons.nicovi...)
Caravan
[Materials]
VOICEVOX:ずんだもん
VOICEVOX:四国めたん
立ち絵(坂本アヒル様)
効果音ラボ
みんちりえ
pixabay
#math
9 сен 2024