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A202501
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Decimal expansion of x satisfying x=e^(-Pi*x/2).
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5
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4, 7, 4, 5, 4, 0, 9, 9, 9, 5, 1, 2, 6, 5, 1, 1, 2, 3, 0, 1, 7, 4, 6, 7, 9, 4, 4, 0, 4, 8, 2, 1, 2, 4, 5, 1, 1, 4, 9, 1, 0, 7, 6, 8, 0, 6, 5, 9, 9, 2, 6, 7, 1, 4, 0, 9, 8, 1, 3, 7, 9, 7, 2, 2, 7, 0, 6, 8, 8, 5, 5, 9, 8, 9, 9, 3, 3, 0, 8, 8, 5, 9, 8, 3, 1, 1, 4, 9, 3, 2, 0, 7, 0, 0, 5, 9, 0, 5, 9
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OFFSET
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0,1
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COMMENTS
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See A202348 for a guide to related sequences. The Mathematica program includes a graph.
Also the only solution of x=I^(x*I), since I^I = exp(-Pi/2). Also the infinite power tower (tetration) of I^I, i.e., the convergent sequence I^(I*I^(I*I^(...(I*I^I)...))). Also LambertW(Pi/2)/(Pi/2). - Stanislav Sykora, Nov 06 2013
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LINKS
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Steven R. Finch, Tauberian Constants, August 30, 2004 [Cached copy, with permission of the author]
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EXAMPLE
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x=0.474540999512651123017467944048212451149107680...
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MATHEMATICA
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u = -Pi/2; v = 0;
f[x_] := x; g[x_] := E^(u*x + v)
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
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PROG
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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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