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
KEYWORD
cons,nonn
AUTHOR
Jonathan Vos Post, Jun 04 2008
STATUS
approved