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Eugine_Nier comments on Welcome to Less Wrong! (2010-2011) - Less Wrong
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More precisely there is a 2-dimensional parameter space of functions that are their own second derivative, i.e., any function of the form Ae^x+Be^-x for any constants A and B.
Is there a generic form of that for any nth derivative?
Yes.
Sum over integers k from 1 to n of A(k)*e^(e^(2*i*pi/k)*x) is its own nth derivative, for all A.