Comment on 100 Years to Solve an Integral (2020)parentComments−abetusk1yA question I hadn't even thought to ask, thanks.So, basically, the eigenfunctions of the Fourier transform are Hermite polynomials times a Gaussian [0] [1].[0] https://math.stackexchange.com/questions/728670/functions-th...[1] https://en.wikipedia.org/wiki/Hermite_polynomials#Hermite_fu...−perihelions1yAs well as the linear combinations (including infinite sums!) of Hermite functions with the same eigenvalue under the Fourier transform. (Those eigenvalues are infinitely degenerate). You could express sech(x) as such a sum.
Comments
A question I hadn't even thought to ask, thanks.
So, basically, the eigenfunctions of the Fourier transform are Hermite polynomials times a Gaussian [0] [1].
[0] https://math.stackexchange.com/questions/728670/functions-th...
[1] https://en.wikipedia.org/wiki/Hermite_polynomials#Hermite_fu...
As well as the linear combinations (including infinite sums!) of Hermite functions with the same eigenvalue under the Fourier transform. (Those eigenvalues are infinitely degenerate). You could express sech(x) as such a sum.