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Taylor-Dirichlet conversion
I just found a simple way to convert between a Taylor series at 0 and a Dirichlet series.
This requires a fractional differintegral.

For any function with :

Pretty cool, huh?

Using this conversion, the Riemann Zeta function can be expressed as:
which I believe is somewhat well known due to its connection with Bernoulli polynomials, and 1/(1 - e^z) is well known to be the generating function for Bernoulli polynomials. Still, I've never seen this formula before, it is interesting to see it like this.
Hmm. If the above is true, then
(which is false)

is the actual result.

So I must have made a slight mistake... I'll have to think on this.

However, a similar form gives:


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