A247675 Decimal expansion of the integral over the square [-1,1]x[-1,1] of 1/sqrt(1+x^2+y^2) dx dy.

3, 1, 7, 3, 4, 3, 6, 4, 8, 5, 3, 0, 6, 0, 7, 1, 3, 4, 2, 1, 9, 1, 7, 5, 6, 4, 6, 7, 0, 4, 5, 5, 3, 8, 5, 1, 9, 9, 7, 6, 4, 8, 1, 6, 1, 9, 6, 1, 9, 9, 9, 5, 3, 7, 1, 7, 5, 7, 2, 5, 9, 2, 9, 9, 4, 7, 6, 6, 2, 9, 8, 0, 4, 1, 4, 1, 6, 3, 6, 5, 7, 1, 8, 7, 8, 1, 8, 6, 1, 7, 0, 2, 3, 8, 9, 9, 5, 7, 5, 5, 5, 7, 1

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

D. H. Bailey, J. M. Borwein, Highly Parallel, High-Precision Numerical Integration p. 9. (2005) Lawrence Berkeley National Laboratory

Formula

Equals 4*log(2 + sqrt(3)) - 2*Pi/3.

Example

3.17343648530607134219175646704553851997648161961999537...

Mathematica

RealDigits[4*Log[2 + Sqrt[3]] - 2*Pi/3, 10, 103] // First

Prog

(PARI) default(realprecision, 100); 4*log(2 + sqrt(3)) - 2*Pi/3 \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 4*Log(2 + Sqrt(3)) - 2*Pi(R)/3; // G. C. Greubel, Aug 31 2018

Crossrefs

Cf. A244921, A247674.

Sequence in context: A135540 A161942 A370689 * A053092 A212045 A292849

Adjacent sequences: A247672 A247673 A247674 * A247676 A247677 A247678

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 22 2014

Status

approved