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

Author

Eric W. Weisstein, Sep 28 2003

Keywords

• nonn
• cons

Examples

			1.404575934663742032773958471548143743234611830652711936118...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 3.11, p. 237.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Grothendieck's Constant.

Crossrefs

Cf. A088367, A088373, A088374.

Programs

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 *)

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

Formula

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