They're infinitely differentiable and any derivative decays faster than any power of X. I will write that down. First of all, Phi of X is infinitely differentiable, so as smooth as you could want, has as many derivatives as you could want and more, differentiable and secondly that, as I said, any derivative decreases faster than any power of X. For any M and N greater than or equal to zero, X to the ND N DX to the [inaudible] derivative of Phi of X [inaudible] also tends to zero as X tends to plus or minus infinity. Those two properties. This is the M. M and N are independent here, so this says – there's nothing mysterious here. See the whole transcript at [[http://see.stanford.edu/materials/lsoftaee261/transcripts/TheFourierTransformAndItsApplications-Lecture12.pdf|The Fourier Transform and its Applications Co - Lecture 12]]

Brad G. Osgood @VideoLectures.net