= 27d567bc2d48d9f40e9ccc20ea370b15)
Perplexed comments on Welcome to Less Wrong! (2010-2011) - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (796)
Following up to EY's comment:
e^x is its own second derivative too. There are two functions that are their own second derivative, and four which are their own fourth derivative.
Cool! So what are the other two (out of three) functions that are their own third derivative? What does their graph look like? And does all this have anything to do with Laplace transforms? Does a sufficiently smooth function have a 1.5th derivative?
Yes, welcome to LW.
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.
I think so.