Almost Convergence.

The title of my last post "Almost Cauchy Sequence" made me wonder if "Almost Cauchy" was already defined in some formal sense. I could not find much on "Almost Cauchy" ... but I did find out about "Almost Convergence." (I think I have ran in to this before... but it is very neat... observe:) A […]

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Several series for powers of pi.

The Weierstrass factorization theorem gives us this identity: Take the left side: Thinking of this in a combinatorial way we can expand it. Each even power of q has a sum of combinations of the inverse squares as its coefficient. That is: Now on the right side of Expand using the Taylor series for the […]

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Quick thought. (Very rough.)

The coefficient of the term will be the number of partitions of n into distinct parts. (It is also the number of partitions in to odd parts as one can prove these are the same using a neat argument with Ferris graphs. ) Now this is the generating function for partitions into distinct parts from […]

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