OFFSET
0,1
REFERENCES
Stephen Fletcher Hewson, A Mathematical Bridge: An Intuitive Journey In Higher Mathematics, World Scientific, NJ, 2003, p. 83.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Rick Kreminski, Using Simpson's rule to approximate sums of infinite series, Coll. Math. J. 28 (5) (1997), p 368-376, Table 1.
Eric Weisstein's World of Mathematics, Zeta Function.
FORMULA
A265162/A113024 = gamma/2 + Pi/4 - (1/2 + sqrt(2))*log(2) + log(Pi)/2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 03 2015
Equals -zeta(1/2, 1/2). - Peter Luschny, Nov 03 2020
EXAMPLE
1 - 1/sqrt(2) + 1/sqrt(3) - 1/sqrt(4) + 1/sqrt(5) - 1/sqrt(6) + 1/sqrt(7) ... =
0.60489864342163037024726591423595549975976254513024738037854664808...
MATHEMATICA
RealDigits[(1 - Sqrt[2])Zeta[1/2], 10, 111][[1]]
PROG
(PARI) (1-sqrt(2))*zeta(1/2) \\ G. C. Greubel, Apr 09 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Oct 11 2005
STATUS
approved