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3 questions
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Fractional integrals and $\sum f(n) n^x$
Preamble
The following is a rather unrigorous way to obtain the Euler-Maclaurin formula. Consider some $\sum_{n=1}^\infty f(n)$. We may rewrite this as
$$\sum_{n=1}^\infty f(n)=\sum_{n=1}^\infty \sum_{...
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5
votes
3
answers
343
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Evaluating the series $\sum_{n=0}^{\infty} n! x^n$ and inverse variable-fractional-derivatives
So I was interested in formally assigning values to the completely divergent series $G(x) = \sum_{n=0}^{\infty} n!x^n $. I guess the question COULD end here if you already have an idea of how to ...
- 2,689
3
votes
1
answer
578
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What is the (fractional) half-derivative of zeta at $s=0$ (and how to compute it)?
(I asked this in MSE before but there was only a general reference which did not help for my specific question)
I think I understood the concept of fractional derivatives applied to ...
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