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Zolotarev-Schur Constant

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The Zolotarev-Schur constant is given by

sigma=1/(c^2)[1-(E(c))/(K(c))]^2
(1)
=0.3110788667048...
(2)

(OEIS A143295), where K(c) is a complete elliptic integral of the first kind and E(c) is a complete elliptic integral of the second kind, and c is the unique solution of the equation

[K(c)-E(c)]^3+(1-c^2)K(c)-(1+c^2)E(c)=0
(3)

with 0<c<1, namely

c=0.9155020553...
(4)

(OEIS A143296).

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References

Finch, S. R. "Zolotarev-Schur Constant." §3.9 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 229-231, 2003.Sloane, N. J. A. Sequences A143295 and A143296 in "The On-Line Encyclopedia of Integer Sequences."

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Zolotarev-Schur Constant

Cite this as:

Weisstein, Eric W. "Zolotarev-Schur Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Zolotarev-SchurConstant.html

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