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 A273100 Decimal expansion of tau_2 (so named by S. Finch), the sum of squared eigenvalues of the Ruelle-Mayer linear operator G_2. 0
 1, 1, 0, 3, 8, 3, 9, 6, 5, 3, 6, 1, 7, 6, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 2.17.1 Ruelle-Mayer Operators, p. 153. LINKS 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

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Last modified July 29 07:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)