A277067 Decimal expansion of value of x such that the solution y to the equation x^y = y has equal real and imaginary parts.
7, 5, 0, 0, 4, 5, 2, 5, 6, 4, 6, 0, 1, 5, 1, 7, 1, 1, 2, 3, 7, 8, 5, 2, 9, 9, 3, 0, 3, 6, 8, 2, 2, 4, 1, 5, 5, 2, 5, 2, 1, 0, 9, 6, 1, 0, 7, 5, 1, 4, 7, 2, 5, 0, 9, 3, 7, 2, 0, 5, 3, 1, 7, 9, 8, 2, 7, 9, 3, 7, 7, 4, 6, 5, 3, 7, 8, 1, 1, 3, 7, 8, 4, 0, 8, 2, 1, 1, 7, 4, 9, 2, 1, 1, 6, 1, 5, 9, 4, 8, 7, 8, 3
Offset: 0
Examples
-0.750045256460151711237852993036822415525210961075147250937205...
Programs
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Mathematica
FindRoot[Re[-ProductLog[-Log[x]]/Log[x]] - Im[-ProductLog[-Log[x]]/Log[x]], {x, -0.76, -0.74}, WorkingPrecision -> 261]
Formula
The solution to x^y=y is y=-ProductLog(-log(x))/log(x).
Comments