login
A143295
Decimal expansion of the Zolotarev-Schur constant.
1
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
OFFSET
0,1
COMMENTS
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
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, 229-231.
LINKS
Paul Erdős and Gábor Szegő, On a problem of I. Schur, Ann.Math., Vol. 43, No. 3 (1942), pp. 451-470; alternative link.
Heinz-Joachim Rack, The first Zolotarev case in the Erdös-Szegö solution to a Markov-type extremal problem of Schur, Univ.Babes-Bolyai Math., Vol. 62, No. 2 (2017), pp. 151-162.
Eric Weisstein's World of Mathematics, Zolotarev-Schur Constant.
EXAMPLE
0.31107886670481920902...
MATHEMATICA
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 *)
CROSSREFS
Cf. A143296.
Sequence in context: A175946 A115378 A120060 * A330892 A289978 A185983
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 05 2008
STATUS
approved