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A140133
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Decimal expansion of the area enclosed in the lens-shaped region of the Laplace Limit.
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0
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1, 8, 5, 3, 2, 6, 8, 4, 4, 8, 7, 0, 7, 9, 8, 7, 0, 3, 3, 2, 2, 1, 9, 3, 6, 4, 0, 3, 4, 3, 9, 7, 2, 7, 8, 8, 7, 9, 4, 6, 9, 6, 5, 3, 8, 9, 6, 3, 2, 5, 4, 6, 4, 0, 1, 3, 5, 5, 7, 8, 1, 0, 0, 2, 0, 6, 7, 8, 7, 9, 7, 3, 6, 5, 0, 8, 5, 1, 6, 6, 2, 7, 1, 1, 7, 1, 3, 3, 4, 8, 8, 5, 5, 6, 9, 0, 2, 5, 8, 8
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OFFSET
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1,2
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COMMENTS
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See Weisstein for complex analysis function.
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LINKS
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EXAMPLE
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1.853268...
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MATHEMATICA
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f[x_] := (Sqrt[x - Tanh[x]]*(x*Csch[x]^2 + 2*x - Coth[x]))/(2* Sqrt[-x + Coth[x]]); xmax = x /. FindRoot[Coth[x] - x == 0, {x, 1}, WorkingPrecision -> 200]; First[ RealDigits[ Chop[ Quiet[ NIntegrate[f[x], {x, 0, xmax}, WorkingPrecision -> 200, MaxRecursion -> 20]]*4], 10, 100]] (* Jean-François Alcover, Jun 07 2012, after D. S. McNeil *)
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PROG
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(Sage)
from mpmath import mp, sqrt, tanh, coth, csch, findroot, quad
mp.dps = 2*dps # safety
def f(x): return 1/2*sqrt(x - tanh(x))*(x*csch(x)^2 + 2*x - coth(x))/sqrt(-x + coth(x))
xmax = findroot(lambda x: coth(x)-x, 1)
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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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