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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| See Weisstein for complex analysis function.
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LINKS
| Eric W. Weisstein, Laplace Limit (value given is incorrect)
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EXAMPLE
| Roughly 1.85298.
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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 1 2011]
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CROSSREFS
| Cf. A033259, A085984.
Sequence in context: A196515 A116397 A176705 * A086723 A011406 A201488
Adjacent sequences: A140130 A140131 A140132 * A140134 A140135 A140136
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KEYWORD
| cons,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 04 2008
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