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proposed
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Number of correct digits of the MRB constant derived from the sequence of partial sums up to m=10^n terms as defined by S[n]= Sum[(-1)^k*(k^(1/k)-1),{k,m}].
(history; published version)
(history; published version)
STATUS
editing
proposed
LINKS
Eric W. Weisstein, 's World of Mathematics, <a href="http://mathworld.wolfram.com/MRBConstant.html">MRB Constant</a>, Mathworld.
EXAMPLE
For n=1, a(n)=1 because after 10^1 partial sums of -1+sqrt(2)-3^(1/3)+4^(1/4)... you get one accurate digit of the MRB constant. For n=2, a(n)=2 because after 10^2 partial sums you get two accurate digits and so on.
For n=2, a(n)=2 because after 10^2 partial sums you get two accurate digits and so on.
REFERENCES
Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, "Convergence Acceleration of Alternating Series", Experimental Mathematics, 9:1 (2000).
LINKS
Henri Cohen, Fernando Rodriguez Villegas and Don Zagier, <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-9/issue-1/Convergence-acceleration-of-alternating-series/em/1046889587.full">Convergence Acceleration of Alternating Series</a>, Experimental Mathematics, 9:1 (2000).
STATUS
approved
editing
STATUS
editing
approved
LINKS
Wikipedia, <a href="http://en.wikipedia.org/wiki/Mathematical_constant">Mathematical constantsconstant</a>
STATUS
approved
editing
STATUS
editing
approved
LINKS
Anonymous, <a href="http://en.wikipedia.org/wiki/Mathematical_constant">Table of selected mathematical constants</a>, Wikipedia.
Wikipedia, <a href="http://en.wikipedia.org/wiki/Mathematical_constant">Mathematical constants</a>
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed