A088367 Decimal expansion of Krivine's bound for Grothendieck's constant, Pi/(2*log(1+sqrt(2))).
1, 7, 8, 2, 2, 1, 3, 9, 7, 8, 1, 9, 1, 3, 6, 9, 1, 1, 1, 7, 7, 4, 4, 1, 3, 4, 5, 2, 9, 7, 2, 5, 4, 9, 3, 4, 0, 7, 9, 1, 7, 3, 1, 9, 0, 9, 7, 7, 3, 2, 3, 9, 3, 8, 1, 0, 2, 4, 9, 5, 9, 9, 5, 6, 8, 8, 5, 1, 5, 4, 1, 2, 8, 7, 6, 3, 7, 8, 4, 0, 8, 0, 2, 4, 3, 1, 6, 7, 6, 6, 3, 5, 7, 8, 2, 5, 5, 3, 0, 8, 9, 3
Offset: 1
Examples
1.7822139781913691117744134529725493407917319097732...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 3.11, pp. 235-237.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..20000
- Noga Alon, Konstantin Makarychev, Yury Makarychev and Assaf Naor, Quadratic forms on graphs, Inventiones Math., Vol. 163 (2006), pp. 499-522; preprint.
- Mark Braverman, Konstantin Makarychev, Yury Makarychev and Assaf Naor, The Grothendieck constant is strictly smaller than Krivine's bound, Forum of Mathematics, Pi, Vol. 1 (2013), e4.
- Jean-Louis Krivine, Sur la constante de Grothendieck, C. R. Acad. Sci. Paris, Series A and B, Vol. 284, No. 8 (1977), pp. A445-A446.
- Simon Plouffe, Grothendieck's majorant.
- Eric Weisstein's World of Mathematics, Grothendieck's Constant.
- Wikipedia, Grothendieck inequality.
Programs
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Magma
SetDefaultRealField(RealField(150)); R:= RealField(); Pi(R)/(2*Log(1 + Sqrt(2))) // G. C. Greubel, Mar 27 2018
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Mathematica
RealDigits[Pi/(2*Log[1 + Sqrt[2]]), 10, 111][[1]] (* Robert G. Wilson v, May 19 2004 *)
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PARI
Pi/(2*log(1 + sqrt(2))) \\ G. C. Greubel, Mar 27 2018
Extensions
Edited by N. J. A. Sloane, Oct 01 2006
Named edited by Amiram Eldar, Jun 24 2021
Comments