In the question
MRB constant proofs wanted ,
I gave the following excerpt from http://marvinrayburns.com/UniversalTOC25.pdf .
.
I accurately worked formula 44 in Matheamatica in the following code.
(*define the eta function*)
eta[s_] := (1 - 2^(1 - s)) Zeta[s];
(*define the higher derivatives of the eta(0)*)
a[i_] := Derivative[i][eta][0];
(*Define c:*)
c[j_] := Sum[Binomial[j, d](-1)^dd^(j - d), {d, 1, j}]
(*formula (44)*)
N[Sum[c[m]/m!*a[m], {m, 1, 40}], 100]
It gave -0.1878587... .
Can anyone come up with a more lucrative program for formula 44 in Mathematica or Maple?
N[Sum[c[m]/m!*a[m], {m, 1, 40}], 100] is an overkill on working precision and too finite to give much accuracy. N[Sum[c[m]/m!*a[m], {m, 1, Infinity}], 10] is better but takes several hours to compute, if it ever gives an solution!
The bottom line is the Mathematica code clearly shows (44) needs an overall minus in front of the summation.