A246687 Decimal expansion of integral_{0..infinity} x*log(x)*(1-eta(x)^2) dx, where the function 'eta' is a solution of the Painlevé III differential equation.

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 402.

Links

Table of n, a(n) for n=0..104.

Formula

1/4 + (7/12)*log(2) - 3*log(A) where A is the Glaisher-Kinkelin constant.

Example

-0.0919275757747180238150402432110722635814007292954564527625...

Mathematica

Join[{0}, RealDigits[1/4 + (7/12)*Log[2] - 3*Log[Glaisher], 10, 104] // First]

Crossrefs

Cf. A074962.

Sequence in context: A280375 A067617 A230458 * A021525 A371935 A297013

Adjacent sequences: A246684 A246685 A246686 * A246688 A246689 A246690

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 01 2014

Status

approved