I'm really not a π day hater, but I do roll my eyes when I read articles exclaiming π "goes on forever!" as if that is a rare and notable property that makes it unique among numbers. I mean, 1/3 "goes on forever" too.
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Replying to @divbyzero
What's really needed is a better appreciation of Gotthold Eisenstein's penetrating analysis of functions of period 1. When everyone knows the wonders lurking in ... + 1/(x - 2) +1/(x - 1) + 1/x + 1/(x + 1) + 1/(x + 2) + ... then we will indeed all have cause to celebrate.
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Replying to @MathPrinceps @divbyzero
That's pi*cot(pi*x), you can prove it using complex analysis
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Replying to @akivaw @divbyzero
That's not how Eisenstein did it, though. And that you need not do it that way is interesting. Significant, even. As Andre Weil noted, with evident admiration.
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Could you please direct me to a source for this? I would like to learn but don't know what paper/book to seek out.
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The canonical reference here is Andre Weil's brilliant little book, ELLIPTIC FUNCTIONS ACCORDING TO EISENSTEIN AND KRONECKER. But this is a very demanding exposition, with few helpful hints likely to encourage the beginner. I'll have to brood to come up with something better.
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