A140133 Decimal expansion of the area enclosed in the lens-shaped region of the Laplace Limit.

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

Offset

1,2

Comments

See Weisstein for complex analysis function.

Links

G. C. Greubel, Table of n, a(n) for n = 1..3000

Eric W. Weisstein, Laplace Limit (value given is incorrect)

Example

1.8532684487079870332219364034397278879469653896325464...

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