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A346205
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Decimal expansion of solution to LambertW(-x) - LambertW(-1,-x) = 2.
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1
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2, 2, 8, 8, 9, 8, 9, 4, 8, 1, 9, 6, 1, 7, 8, 6, 4, 1, 2, 3, 6, 6, 3, 6, 1, 2, 5, 3, 7, 2, 2, 0, 5, 5, 3, 5, 6, 3, 4, 2, 6, 2, 8, 2, 7, 1, 8, 1, 4, 6, 2, 6, 2, 3, 6, 6, 7, 6, 7, 7, 7, 6, 6, 1, 4, 4, 4, 1, 3, 2, 0, 3, 0, 2, 2, 3, 1, 9, 6, 9, 7, 1, 3, 6, 7, 8, 3, 1, 5, 3, 2, 3, 7, 3, 9, 7, 7, 1, 5, 7, 3, 3, 6, 3, 1, 3, 4, 6, 6, 6
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals 2/(e^2-1)*exp(2/(1-e^2)) = 2/(A072334^2-1)*exp(2/(1-A072334^2)).
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EXAMPLE
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0.2288989481961786412366361253722...
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MATHEMATICA
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x/.FindRoot[LambertW[-x]-LambertW[-1, -x]==2, {x, 0.1, 0.3}, WorkingPrecision -> 110]
RealDigits[2/(E^2-1)*Exp[2/(1-E^2)], 10, 135][[1]] (* G. C. Greubel, Jun 11 2024 *)
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PROG
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(PARI) exp(-cotanh(1))/sinh(1)
(Magma) SetDefaultRealField(RealField(135)); 2/(Exp(2)-1)*Exp(2/(1-Exp(2))); // G. C. Greubel, Jun 11 2024
(SageMath) numerical_approx(2/(e^2-1)*exp(2/(1-e^2)), digits=135) # G. C. Greubel, Jun 11 2024
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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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