if by scale-invariance you mean f(a*x) = a*f(x) then the reason you can't prove it is that it's not true (i made plots)
A Nasty Integral & An Interesting Observation It's interesting that equation (2) is independent of the choice of alpha.. I can't immediately see why this should be true.. I tried proving scale-invariance, but to no avail. Can any of you see why this should be true?pic.twitter.com/yircjqHmG0
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No, that’s linearity and is not true for either sine or exponents. Scale invariance is f(ax)=f(x)
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Right! That’s what my undergrad complex analysis prof
@rsachsgmu said earlier! - 1 more reply
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I thought that too.. but if you work in out and set alpha to zero at the start it works fine
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Come on guys this is trivial. Recall z = exp(i u) = cos(u) + i sin(u). Thenpic.twitter.com/PkxR5OL5yl
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Agreed, as many other's have pointed out the complex plane is the way to go. I personally try to not use complex as much as I can, as it makes the integrals more fun :D
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Beautiful
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