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A244257
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Decimal expansion of the asymptotic evaluation of the constrained maximum of a certain quadratic form.
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0
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2, 3, 9, 7, 9, 4, 5, 5, 8, 6, 1, 1, 4, 4, 3, 6, 3, 3, 7, 4, 0, 6, 1, 3, 9, 3, 7, 8, 9, 0, 6, 0, 6, 6, 0, 5, 5, 8, 8, 0, 8, 2, 3, 4, 0, 0, 1, 5, 7, 6, 3, 1, 1, 6, 0, 3, 1, 1, 1, 4, 9, 9, 7, 9, 3, 5, 1, 9, 1, 3, 6, 8, 6, 7, 9, 7, 6, 4, 5, 1, 9, 8, 5, 5, 7, 4, 8, 7, 9, 1, 1, 9, 5, 9, 4, 3, 3, 3, 7, 7
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OFFSET
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1,1
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COMMENTS
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The quadratic form to maximize is (sum_(k>=1) x(k)/k)^2 + sum_(k>=1) (x(k)/k)^2, subject to the constraint (sum_(k>=1) x(k)^2) <= 1.
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.12 Du Bois Reymond's constants, p. 239.
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LINKS
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FORMULA
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(Pi/xi)^2, where xi is the smallest positive solution of the equation x+tan(x)=0.
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EXAMPLE
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2.397945586114436337406139378906...
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MATHEMATICA
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xi = x /. FindRoot[x + Tan[x] == 0, {x, 2}, WorkingPrecision -> 100]; RealDigits[(Pi/xi)^2] // First
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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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