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 Mar 20 comment Unable to reproduce this figure Not Alpha, here try it online Mar 20 comment Unable to reproduce this figure I tried the formula with Wolfram and it looks pretty similar, so it is correct. Not a Matlab expert, but probably you need some more precision with contour plot, as I had problems with it also. Or just specify explicitly what contour levels to plot, try $1/e^{10}, 1/e^{20}, 1/e^{30}, \dots$. Oct 1 awarded Yearling Sep 29 awarded Nice Answer Feb 10 awarded Nice Answer Jan 30 awarded Notable Question Dec 20 awarded Caucus Dec 20 awarded Constituent Oct 25 awarded Tumbleweed Oct 1 awarded Yearling Sep 24 awarded Autobiographer Jul 22 awarded Good Answer Feb 25 awarded Nice Question Nov 17 awarded Popular Question Nov 7 comment What are some examples of notation that really improved mathematics? @NateEldredge I think it is an improvement. Compare vector expressed as a series in usual notation $\sum \langle x,\phi \rangle \phi$ and in bra-ket notation $\sum \langle \phi | x \rangle |\phi\rangle$. The bra-ket notation also can be read not just as sum of vectors with coefficients but also as matrix-vector multiplication just by swapping things around. Also we can treat $\sum |\phi\rangle\langle\phi |$ as an identity and it gives rise to a bunch of useful algebraic manipulations. Nov 7 answered What are some examples of notation that really improved mathematics? Nov 7 comment What are some examples of notation that really improved mathematics? Einstein's notation is indeed the power of math at its finest! I would add Kronecker and Levi-Civita symbols to this answer. Nov 7 awarded Nice Answer Nov 7 comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? @kriss Thx, next to last was wrong indeed (also the second one), counting to five is hard! Fixed it and also colored the pens for more clearity. Nov 7 revised How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? added 2 characters in body