A244091 Decimal expansion of sqrt(3)/(2*(sqrt(2)-1))^(1/3), the Landau-Kolmogorov constant C(3,1) for derivatives in L_2(0, infinity).

1, 8, 4, 4, 2, 0, 4, 9, 8, 0, 6, 3, 3, 3, 9, 3, 6, 9, 1, 7, 0, 5, 6, 9, 0, 5, 4, 7, 4, 9, 4, 1, 2, 9, 9, 6, 8, 7, 9, 9, 6, 8, 8, 3, 9, 3, 0, 7, 3, 0, 1, 8, 2, 2, 0, 3, 8, 8, 4, 4, 9, 5, 6, 8, 9, 7, 0, 1, 1, 5, 5, 2, 9, 0, 3, 3, 5, 0, 5, 5, 1, 0, 8, 5, 9, 5, 3, 5, 7, 8, 0, 7, 5, 7, 4, 7, 6, 2, 0, 5

Offset: 1

Author

Jean-François Alcover, Jun 20 2014

Keywords

• nonn
• cons
• easy

Comments

The corresponding Landau-Kolmogorov inequality is ||f'|| <= C(3,1) ||f||^(2/3) ||f'''||^(1/3) where the real-valued function f is defined on the half-line (0,infinity), the involved norm being ||f|| = (integral_(0..infinity) f(x)^2 dx)^(1/2).

Examples

			1.84420498063339369170569...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 214.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Landau-Kolmogorov Constants
• Index entries for algebraic numbers, degree 12.

Programs

Mathematica

RealDigits[ Sqrt[3]/(2*(Sqrt[2] - 1))^(1/3), 10, 100][[1]]

PARI

sqrt(3)/(2*(sqrt(2)-1))^(1/3) \\ G. C. Greubel, Jul 05 2017