A273100 Decimal expansion of tau_2 (so named by S. Finch), the sum of squared eigenvalues of the Ruelle-Mayer linear operator G_2.

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

Offset

1,4

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 2.17.1 Ruelle-Mayer Operators, p. 153.

Links

Table of n, a(n) for n=1..16.

Formula

Integral_{0..inf} Integral_{0..inf} J_1(2*sqrt(u*v)^2 / ((exp(u)-1) * (exp(v)-1)) du dv, where J_1 is the Bessel function of the first kind with parameter 1.

Example

1.103839653617613...

Mathematica

digits = 16; m0 = 100; dm = 5; Clear[f];
f[m_] := f[m] = NIntegrate[BesselJ[1, 2*Sqrt[u*v]]^2/((Exp[u]-1) * (Exp[v]-1)), {u, 0, m}, {v, 0, m - u}, MaxRecursion -> 30, WorkingPrecision -> digits + 10]; f[m = m0]; Print[m, " ", RealDigits[f[m], 10, digits][[1]]]; f[m = m0 + dm]; Print[m, " ", RealDigits[f[m], 10, digits][[1]]]; While[RealDigits[f[m], 10, digits][[1]] != RealDigits[f[m - dm], 10, digits][[1]], m = m + dm; Print[m, " ", RealDigits[f[m], 10, digits][[1]]]]; RealDigits[f[m], 10, digits][[1]]

Crossrefs

Cf. A038517, A242914.

Sequence in context: A106230 A205126 A016623 * A046543 A233129 A035292

Adjacent sequences: A273097 A273098 A273099 * A273101 A273102 A273103

Keyword

nonn,cons,more

Author

Jean-François Alcover, May 15 2016

Status

approved