This equality holds for *all* real numbers N,M 
Can you see why?pic.twitter.com/LvR2r0y6iT
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Beautiful solution by
@ValFadeev. As you can see, the trick is showing that the integral *does not* depend on N.pic.twitter.com/vOJFq5BCNQ
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Just to elucidate how counterintuitive this result is, I've plotted the integrand for different values of N.
All of these curves must admit the EXACT same area!pic.twitter.com/03EsDf4QD9
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Time ago in an interview for a job I was asked the area of the Gaussian and I was so nervous that I resorted to this trick instead of recalling it from memory.
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that's badass
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looks like it behaves a bit like some of the exponential family of distributions like the Weibull distribution - is that a coincidence?
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Well this identity defines a family of pdfs with polynomial tails. This is kinda like a fat-tailed Gamma for negative N, and a student-t for positive N. Idk if it has a name
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