A088375 Decimal expansion of a postulated upper estimate for the complex Grothendieck constant.

1, 4, 0, 4, 5, 7, 5, 9, 3, 4, 6, 6, 3, 7, 4, 2, 0, 3, 2, 7, 7, 3, 9, 5, 8, 4, 7, 1, 5, 4, 8, 1, 4, 3, 7, 4, 3, 2, 3, 4, 6, 1, 1, 8, 3, 0, 6, 5, 2, 7, 1, 1, 9, 3, 6, 1, 1, 8, 0, 8, 9, 6, 1, 8, 5, 8, 7, 7, 1, 7, 1, 9, 4, 4, 8, 2, 5, 7, 7, 2, 2, 9, 8, 6, 5, 2, 8, 9, 8, 6, 2, 7, 0, 8, 7, 4, 4, 7, 8, 9, 3, 5

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Grothendieck's Constant

Formula

Equals (sqrt(8*Pi)*Gamma(3/4)^2)/(Pi^2 - 2*Gamma(3/4)^4). - Jan Mangaldan, Nov 23 2020

Example

1.404575934663742032773958471548143743234611830652711936118...

Maple

Re(evalf(1/(2*EllipticK(I)-EllipticE(I)), 120)); # Vaclav Kotesovec, Apr 22 2015

Mathematica

First[ RealDigits[ N[1/(2*EllipticK[-1] - EllipticE[-1] ), 120], 10, 102]](* Jean-François Alcover, Jun 07 2012, after Eric W. Weisstein *)
RealDigits[(Sqrt[8 Pi] Gamma[3/4]^2)/(Pi^2 - 2 Gamma[3/4]^4), 10, 102][[1]] (* Jan Mangaldan, Nov 23 2020 *)

Prog

(PARI) magm(a, b)=my(eps=10^-(default(realprecision)-5), c); while(abs(a-b)>eps, my(z=sqrt((a-c)*(b-c))); [a, b, c] = [(a+b)/2, c+z, c-z]); (a+b)/2
E(x)=Pi/2/agm(1, sqrt(1-x))*magm(1, 1-x)
K(x)=Pi/2/agm(1, sqrt(1-x))
1/(2*K(-1)-E(-1)) \\ Charles R Greathouse IV, Aug 02 2018

Crossrefs

Cf. A088367, A088373, A088374.

Sequence in context: A258859 A258860 A134944 * A217220 A361620 A303560

Adjacent sequences: A088372 A088373 A088374 * A088376 A088377 A088378

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 28 2003

Status

approved