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A143295
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Decimal expansion of the Zolotarev-Schur constant.
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1
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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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
Named after the Russian mathematicians Yegor Ivanovich Zolotarev (1847-1878) and Issai Schur (1875-1941). - Amiram Eldar, Jun 15 2021
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 229-231.
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LINKS
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EXAMPLE
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0.31107886670481920902...
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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