A386733 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} {1/(x+y)} dx dy, where {} denotes fractional part.
5, 6, 3, 8, 2, 7, 3, 2, 7, 6, 9, 5, 7, 7, 7, 4, 0, 0, 5, 9, 8, 2, 5, 6, 6, 5, 9, 5, 9, 3, 3, 4, 0, 5, 4, 1, 5, 4, 1, 5, 2, 5, 3, 1, 8, 1, 1, 7, 1, 1, 1, 2, 8, 9, 3, 7, 3, 5, 8, 0, 9, 0, 4, 3, 0, 1, 7, 8, 3, 5, 0, 8, 7, 3, 7, 7, 8, 8, 9, 9, 4, 2, 9, 4, 9, 1, 2, 2, 0, 3, 6, 8, 2, 9, 5, 8, 0, 2, 2, 4, 3, 2, 0, 0, 0, 8
Offset: 0
Examples
0.56382732769577740059825665959334054154152531811711...
Links
- Ovidui Furdui, Problem 150, Problems, Missouri J. Math. Sci., Vol. 16, No. 2 (2004), p. 130; Huizeng Qin, Solution to Problem 150, ibid., Vol. 17, No. 3 (2005), pp. 197-199.
- Ovidiu Furdui, Multiple Fractional Part Integrals and Euler's Constant, Miskolc Mathematical Notes, Vol. 17, No. 1 (2016), pp. 255-266.
Programs
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Mathematica
RealDigits[2*Log[2] - Pi^2/12, 10, 120][[1]]
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PARI
2*log(2) - zeta(2)/2