login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..100.

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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 21 21:36 EDT 2017. Contains 290908 sequences.