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0 votes
1 answer
255 views

Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x $ at integer x?

[This question is copied from math.stackexchange, it didn't get answers so far] For some exercises with (divergent) summation of the Stieltjes constants,see also MSE I'm trying a formula, which …
Gottfried Helms's user avatar
5 votes
1 answer
732 views

mertens-function in the light of divergent summation - what summation method were best adapted

Just reading about the Mertens-function in the other thread Mertens function I remember an earlier attempt to apply divergent summation to the series which is constructed of the Moebius-function at …
Gottfried Helms's user avatar
0 votes
0 answers
159 views

Is there an option to handle Neumann-series when it diverges? (using infinite-sized Carleman...

(I asked this in MSE but did not find resonance, there is also a relation to an older discussion here on summability see here and a followup formulating an $\text{ais}()$ already here) Mot …
Gottfried Helms's user avatar
6 votes
1 answer
454 views

Efficient (divergent) summation for sum of zetas at negative arguments?

In a question in MSE (see bottom of my own answer) I'm considering the following series, depending on a parameter m: $$ L(m) = -\zeta(1m)/1 - \zeta(2m)/2 - \zeta(3m)/3 - \ldots $$ where I want to make …
Gottfried Helms's user avatar
4 votes
1 answer
443 views

Is that series-transformation known in the context of divergent summation?

Note: I asked this question in math.stackexchange but did not receive an answer Background: In the context of divergent summation I'm analyzing the matrix of eulerian numbers for a regular matrix …
Gottfried Helms's user avatar
13 votes
1 answer
778 views

Cesaro(?)/Euler(?) - summation of the $s(p)=\sum_{k=0}^\infty (-1)^{H(k)} (1+k)^p$ for $p=1,...

In another thread (in MO) there was a question about a series where the signs at the terms alternate with the "Hamming-weight", that means according to the number of bits in the binary representation …
Gottfried Helms's user avatar
3 votes
1 answer
577 views

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 monomial …
Gottfried Helms's user avatar