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A366072
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Decimal expansion of a constant related to the asymptotics of A307399.
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1
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5, 8, 4, 2, 7, 8, 3, 2, 1, 4, 7, 6, 3, 5, 2, 0, 3, 2, 8, 4, 7, 3, 5, 0, 4, 2, 9, 2, 5, 3, 6, 4, 3, 5, 0, 9, 0, 3, 3, 4, 1, 7, 8, 0, 0, 7, 7, 3, 2, 8, 4, 0, 6, 1, 8, 4, 5, 7, 7, 4, 2, 4, 3, 5, 5, 8, 8, 2, 0, 3, 1, 4, 0, 9, 8, 5, 9, 2, 7, 0, 5, 3, 7, 5, 2, 1, 4, 2, 8, 3, 5, 6, 2, 2, 5, 0, 6, 4, 3, 0, 0, 1, 4, 3, 4
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals limit n->infinity A307399(n)^(1/n).
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EXAMPLE
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5.84278321476352032847350429253643509033417800773284061845774243558820314...
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MATHEMATICA
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val = r /. FindRoot[{1 + (Log[1 - r*s] + QPolyGamma[0, 1, r*s])/Log[r*s] == s + r*s*Derivative[0, 1][QPochhammer][r*s, r*s] / QPochhammer[r*s], (-4*r*s*ArcTanh[1 - 2*r*s] + s*(1 - r*s)*Log[r*s]^2 + 2*Log[1 - r*s]) / (-1 + r*s) - 2*QPolyGamma[0, 1, r*s] + ((1 - s)*Log[r*s] + Log[1 - r*s] + QPolyGamma[0, 1, r*s])^2 - QPolyGamma[1, 1, r*s] + 2*r*s*Log[r*s]*Derivative[0, 0, 1][QPolyGamma][0, 1, r*s] == (-1 + 1/s + Log[1 - r*s]/(s*Log[r*s]) + QPolyGamma[0, 1, r*s]/(s*Log[r*s]) + r^2*s*Derivative[0, 2][QPochhammer][r*s, r*s] / QPochhammer[r*s])*s* Log[r*s]^2}, {r, 1/6}, {s, 2}, WorkingPrecision -> 90]; N[1/Chop[val], -Floor[Log[10, Abs[Im[val]]]] - 3]
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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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