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A207528
Decimal expansion of 4th du Bois-Reymond constant.
8
0, 0, 5, 2, 4, 0, 7, 0, 4, 6, 7, 7, 7, 0, 4, 7, 7, 1, 1, 4, 8, 5, 6, 8, 9, 2, 0, 0, 7, 0, 1, 0, 5, 8, 9, 3, 7, 5, 8, 6, 8, 4, 3, 4, 4, 5, 5, 0, 8, 3, 4, 9, 2, 8, 6, 8, 4, 7, 6, 0, 3, 3, 3, 5, 5, 7, 9, 2, 0, 8, 6, 4, 4, 5, 2, 4, 5, 4, 8, 0, 3, 5, 1, 7, 4, 6, 6, 3, 2, 7, 7, 0, 3, 5, 3, 0, 8
OFFSET
0,3
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 237-239.
LINKS
Eric Weisstein's World of Mathematics, du Bois-Reymond Constants.
FORMULA
2*Sum_{k>=1} (1 + (x_k)^2)^(-2) = (e^4 - 4*e^2 - 25)/8, where x_k is the k-th root of t = tan t and e = 2.71828... is the natural logarithm base.
EXAMPLE
0.0052407046777047711...
MATHEMATICA
RealDigits[(E^4 - 4E^2 - 25)/8, 10, 100][[1]]
CROSSREFS
Cf. A138730 (continued fraction expansion).
Cf. A062546 (c2), A224196 (c3), A243108 (c5), A245333 (c6).
Sequence in context: A277581 A307381 A256167 * A019901 A187059 A267120
KEYWORD
nonn,cons
AUTHOR
Alonso del Arte, Feb 24 2012
STATUS
approved