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In each k-dimension space there's only one unit sphere. We're summing the volumes of all those spheres for all possible 2k spaces correct ?
For all n (not only evens) it seems this is the result. So taking only the even indices gets rid of the factor (erf()+1) on the RHS.pic.twitter.com/cGQlmq8QFp
The odd counterpart doesn't look as sexy. *correctedpic.twitter.com/R3Birg5R6N
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If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π.
I have no idea why this should be true..
