A143296 Decimal expansion of the transcendental root c used to compute the Zolotarev-Schur constant.

9, 1, 5, 5, 0, 2, 0, 5, 5, 3, 8, 9, 6, 7, 6, 3, 9, 6, 3, 0, 5, 5, 2, 4, 0, 3, 6, 4, 0, 1, 6, 6, 2, 2, 8, 9, 6, 5, 4, 3, 1, 2, 9, 4, 2, 2, 8, 8, 4, 6, 0, 7, 6, 6, 7, 5, 0, 1, 7, 7, 6, 3, 4, 0, 0, 3, 9, 7, 8, 8, 0, 2, 7, 5, 4, 6, 1, 2, 2, 1, 6, 7, 9, 7, 9, 2, 3, 7, 7, 4, 4, 8, 3, 0, 9, 6, 9, 2, 8, 1, 8, 8, 5, 8, 0

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Eric Weisstein's World of Mathematics, Zolotarev-Schur Constant

Example

0.91550205538967639630...

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]; RealDigits[c0, 10, 105] // First (* Jean-François Alcover, Feb 07 2013, after Eric W. Weisstein *)

Prog

(PARI) solve(x=.9, .92, my(e=ellE(x), k=ellK(x)); e^3 - 3*k*e^2 + (x^2 + 3*k^2 + 1)*e + (x^2 - k^2 - 1)*k) \\ Charles R Greathouse IV, Feb 04 2025

Crossrefs

Cf. A143295.

Sequence in context: A100924 A350885 A258268 * A198355 A205326 A021526

Adjacent sequences: A143293 A143294 A143295 * A143297 A143298 A143299

Keyword

nonn,cons,changed

Author

Eric W. Weisstein, Aug 05 2008

Status

approved