A207528 Decimal expansion of 4th du Bois-Reymond constant.

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

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 237-239.

Links

Table of n, a(n) for n=0..96.

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

Adjacent sequences: A207525 A207526 A207527 * A207529 A207530 A207531

Keyword

nonn,cons

Author

Alonso del Arte, Feb 24 2012

Status

approved