Introducing the multi-zeta function!

Contemplating: My friend, and fellow math blogger, Owen, tried to tell me I was dealing with the multi-zeta function the other day, but the very general definition on WolframMathworld left me feeling a little mystified. I could see how the identities I was playing with fit in to it, but what was all of that […]

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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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