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A073007
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Decimal expansion of Varga's constant.
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4
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9, 2, 8, 9, 0, 2, 5, 4, 9, 1, 9, 2, 0, 8, 1, 8, 9, 1, 8, 7, 5, 5, 4, 4, 9, 4, 3, 5, 9, 5, 1, 7, 4, 5, 0, 6, 1, 0, 3, 1, 6, 9, 4, 8, 6, 7, 7, 5, 0, 1, 2, 4, 4, 0, 8, 2, 3, 9, 7, 0, 0, 6, 1, 4, 2, 1, 7, 2, 9, 3, 7, 5, 2, 4, 7, 2, 8, 6, 5, 0, 7, 0, 7, 0, 5, 2, 4, 1, 5, 8, 7, 0, 6, 1, 4, 2, 4, 7, 1, 4, 4
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OFFSET
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1,1
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COMMENTS
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Equals the reciprocal of the one-ninth constant A072558.
Named after the American mathematician Richard Steven Varga (1928-2022). - Amiram Eldar, Jun 22 2021
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REFERENCES
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R. S. Varga, Scientific Computation on Mathematical Problems and Conjectures, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 60, Philadelphia, PA: SIAM, 1990. See Chapter 2, pp. 23-38.
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LINKS
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A. J. Carpenter, A. Ruttan and R. S. Varga, Extended numerical computations on the "1/9" conjecture in rational approximation theory, in: P. R. Graves-Morris, E. B. Saff and R. S. Varga (eds.), Rational approximation and interpolation, Springer, Berlin, Heidelberg, 1984, pp. 383-411; alternative link.
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EXAMPLE
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9.28902549192081891875544943595174506...
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MATHEMATICA
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nmax=250; c = k /. FindRoot[EllipticK[k^2] == 2*EllipticE[k^2], {k, 9/10}, WorkingPrecision -> nmax]; Take[RealDigits[1/N[Exp[-Pi*(EllipticK[1 - c^2]/EllipticK[c^2])], nmax]][[1]], 200] (* G. C. Greubel, Mar 10 2018 *)
RealDigits[v /. FindRoot[4 EllipticE[InverseEllipticNomeQ[1/v]] == Pi EllipticTheta[3, 0, 1/v]^2, {v, 9, 9, 10}, WorkingPrecision -> 101]][[1]] (* Jan Mangaldan, Jun 25 2020 *)
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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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