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 A140133 Decimal expansion of the area enclosed in the lens-shaped region of the Laplace Limit. 0
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See Weisstein for complex analysis function. LINKS Eric W. Weisstein, Laplace Limit (value given is incorrect) EXAMPLE 1.853268... MATHEMATICA 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 *) PROG (Sage) def A140133_cons(dps=200):     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)     return quad(f, [0, xmax])*4  # [D. S. McNeil, Feb 01 2011] CROSSREFS Cf. A033259, A085984. Sequence in context: A116397 A275306 A176705 * A086723 A011406 A201488 Adjacent sequences:  A140130 A140131 A140132 * A140134 A140135 A140136 KEYWORD cons,nonn AUTHOR Jonathan Vos Post, Jun 04 2008 STATUS approved

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