A way to derive this is to take the Fourier Coefficients of cosh(x/π) and work from there https://math.stackexchange.com/questions/2368614/calculate-%E2%88%91-k0-1n-1k2%CF%802/2368657#2368657 …pic.twitter.com/Z3TTluJlK3
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A way to derive this is to take the Fourier Coefficients of cosh(x/π) and work from there https://math.stackexchange.com/questions/2368614/calculate-%E2%88%91-k0-1n-1k2%CF%802/2368657#2368657 …pic.twitter.com/Z3TTluJlK3
Very cool.
No credit to the Reddit user who discovered this, then? I browse r/math too.
I hardly think it was a Reddit user who discovered this, it may have been posted there.
Continued fraction for 2/(e²-1) is mindboggling. Just odd numbers > 1. Ultimate beauty of continued fractionpic.twitter.com/P63adHtZhY
>>> import torch, math >>> ((torch.arange(1, 1e8, dtype = torch.float64) * math.pi)**2 + 1).pow(-1).sum().item() 0.15651764173645402 >>> 1/(math.e**2 - 1) 0.15651764274966568
Does anyone know why this works? Why are they connected?
By infinite series expansions.
You certainly know that e^iπ+1=0 too! 
Do you have the proof ? I am curious.
Fourier series ( cosh(a*x) for x in [-Pi,Pi], a=1/Pi)
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