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A242914
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Decimal expansion of the trace of the Ruelle-Mayer linear operator G_2.
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1
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7, 7, 1, 1, 2, 5, 5, 2, 3, 6, 5, 5, 6, 5, 8, 9, 0, 9, 3, 1, 7, 3, 1, 7, 7, 6, 3, 2, 7, 7, 7, 0, 6, 8, 8, 5, 9, 2, 1, 6, 7, 8, 3, 8, 8, 2, 1, 1, 3, 6, 1, 2, 3, 2, 6, 2, 6, 9, 2, 6, 0, 0, 9, 6, 3, 5, 4, 7, 4, 7, 4, 0, 9, 1, 4, 9, 1, 8, 6, 0, 3, 8, 9, 3, 7, 2, 3, 9, 4, 0, 1, 4, 6, 9, 1, 2, 6, 5, 5, 9, 3, 6, 8, 9
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OFFSET
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0,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 2.17.1 Ruelle-Mayer Operators, p. 153.
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LINKS
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FORMULA
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1/2-1/(2*sqrt(5))+1/2*sum_(k>0) (-1)^(k-1)*binomial(2*k,k)*(zeta(2*k)-1)
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EXAMPLE
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0.7711255236556589093173177632777...
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MATHEMATICA
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NIntegrate[BesselJ[1, 2*x]/(Exp[x]-1), {x, 0, Infinity}, WorkingPrecision -> 140] // RealDigits[#, 10, 80]& // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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