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A072558 Decimal expansion of One-ninth constant. 5
1, 0, 7, 6, 5, 3, 9, 1, 9, 2, 2, 6, 4, 8, 4, 5, 7, 6, 6, 1, 5, 3, 2, 3, 4, 4, 5, 0, 9, 0, 9, 4, 7, 1, 9, 0, 5, 8, 7, 9, 7, 6, 5, 6, 3, 2, 9, 0, 1, 1, 5, 0, 8, 6, 6, 9, 8, 5, 6, 8, 1, 4, 6, 9, 8, 1, 9, 2, 4, 3, 4, 1, 4, 6, 2, 6, 4, 2, 6, 4, 3, 4, 1, 2, 7, 7, 6, 1, 9, 9, 0, 4, 0, 9, 1, 5, 8, 7, 3, 1, 9, 2, 9, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The generating function of A113184 equals 1/8 at q = Lambda = 0.1076539192... where K(k)=2E(k). - Michael Somos, Jul 21 2006

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 259-262.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Steven R. Finch, The "One-Ninth" Constant [Broken link]

Steven R. Finch, The "One-Ninth" Constant [From the Wayback machine]

Alphonse P. Magnus, Jean Meinguet, The elliptic functions and integrals of the '1/9' problem

Alphonse P. Magnus, Jean Meinguet, The elliptic functions and integrals of the '1/9' problem, presented at Antwerpen international conference on rational approximation, 1999, ICRA99, Numerical Algorithms 24: (1-2) (2000) 117-139.

Simon Plouffe, The One-ninth constant

Eric Weisstein's World of Mathematics, One-Ninth Constant

EXAMPLE

0.1076539192264845766153234450909471905879...

MATHEMATICA

c = k /. FindRoot[ EllipticK[k^2] == 2*EllipticE[k^2], {k, 9/10}, WorkingPrecision -> 120]; Take[ RealDigits[ N[Exp[-Pi*(EllipticK[1 - c^2] / EllipticK[c^2])], 120]][[1]], 105] (* Jean-Fran├žois Alcover, Jul 28 2011, after MathWorld *)

CROSSREFS

Cf. A073007, A072559.

Sequence in context: A196553 A244921 A101464 * A022963 A023449 A307338

Adjacent sequences:  A072555 A072556 A072557 * A072559 A072560 A072561

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Aug 03 2002

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)