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%I #20 Jun 15 2021 07:31:05
%S 3,1,1,0,7,8,8,6,6,7,0,4,8,1,9,2,0,9,0,2,7,5,4,6,9,5,9,0,9,1,4,2,1,8,
%T 0,2,6,4,8,9,5,7,1,5,8,4,3,2,8,5,8,6,7,4,5,4,9,4,9,4,9,1,7,0,6,7,9,5,
%U 7,5,2,8,3,1,9,2,0,2,7,5,3,3,0,7,1,2,0,5,2,7,1,6,3,8,4,9,5,1,7,1,5,8,7,0,3
%N Decimal expansion of the Zolotarev-Schur constant.
%C Note that in the Reference P. Erdös and G. Szegö the numerical value of the Zolotarev-Schur constant is given (due to roundings) in the biased form 0.3124... - _Heinz-Joachim Rack_, Oct 03 2017
%C Named after the Russian mathematicians Yegor Ivanovich Zolotarev (1847-1878) and Issai Schur (1875-1941). - _Amiram Eldar_, Jun 15 2021
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 229-231.
%H Paul Erdős and Gábor Szegő, <a href="https://www.jstor.org/stable/1968803">On a problem of I. Schur</a>, Ann.Math., Vol. 43, No. 3 (1942), pp. 451-470; <a href="https://www.renyi.hu/~p_erdos/1942-01.pdf">alternative link</a>.
%H Heinz-Joachim Rack, <a href="http://dx.doi.org/10.24193/subbmath.2017.2.02">The first Zolotarev case in the Erdös-Szegö solution to a Markov-type extremal problem of Schur</a>, Univ.Babes-Bolyai Math., Vol. 62, No. 2 (2017), pp. 151-162.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zolotarev-SchurConstant.html">Zolotarev-Schur Constant</a>.
%e 0.31107886670481920902...
%t c0 = c /. FindRoot[ EllipticE[c^2]^3 - 3*EllipticK[c^2]*EllipticE[c^2]^2 + (c^2 + 3*EllipticK[c^2]^2 + 1)*EllipticE[c^2] + EllipticK[c^2]*(c^2 - EllipticK[c^2]^2 - 1) == 0, {c, 9/10}, WorkingPrecision -> 110]; sigma = (1 - EllipticE[c0^2]/EllipticK[c0^2])^2/c0^2; RealDigits[sigma, 10, 105] // First (* _Jean-François Alcover_, Feb 07 2013, after _Eric W. Weisstein_ *)
%Y Cf. A143296.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Aug 05 2008
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