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A247675
Decimal expansion of the integral over the square [-1,1]x[-1,1] of 1/sqrt(1+x^2+y^2) dx dy.
4
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
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
Sequence in context: A135540 A161942 A370689 * A053092 A212045 A292849
KEYWORD
nonn,cons
AUTHOR
STATUS
approved