A244257 Decimal expansion of the asymptotic evaluation of the constrained maximum of a certain quadratic form.

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

Offset: 1

Author

Jean-François Alcover, Jun 24 2014

Keywords

• nonn
• cons
• easy

Comments

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.

Examples

			2.397945586114436337406139378906...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.12 Du Bois Reymond's constants, p. 239.

Crossrefs

Cf. A196504.

Programs

Mathematica

xi = x /. FindRoot[x + Tan[x] == 0, {x, 2}, WorkingPrecision -> 100]; RealDigits[(Pi/xi)^2] // First

Formula

(Pi/xi)^2, where xi is the smallest positive solution of the equation x+tan(x)=0.