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A258500
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Decimal expansion of the nontrivial real solution of x^(3/2) = (3/2)^x.
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2
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7, 4, 0, 8, 7, 6, 4, 6, 8, 6, 9, 6, 5, 7, 7, 4, 5, 2, 1, 9, 5, 7, 2, 9, 5, 0, 2, 8, 5, 1, 0, 6, 1, 4, 3, 8, 9, 8, 0, 4, 1, 7, 1, 1, 4, 1, 0, 7, 4, 0, 0, 0, 1, 5, 1, 8, 2, 2, 7, 1, 8, 3, 9, 3, 7, 9, 1, 7, 0, 7, 1, 7, 1, 0, 0, 1, 3, 8, 4, 0, 2, 2, 8, 4, 2, 1, 8, 2, 3, 1, 1, 9, 2, 3, 0, 4, 7, 0, 6, 6, 7
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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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x0 = -((x*ProductLog(-1, -(log(x)/x)))/log(x)), with x = 3/2, where ProductLog is the Lambert W function.
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EXAMPLE
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x0 = 7.408764686965774521957295028510614389804171141074...
z = x0^(3/2) = 20.16595073003535058942970947434890012034363496 ...
z > e^e = 15.15426224... = A073226.
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MATHEMATICA
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x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 3/2; RealDigits[x0, 10, 101] // 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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