A245297 Decimal expansion of the Landau-Kolmogorov constant C(5,2) for derivatives in the case L_infinity(infinity, infinity).

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

Offset: 1

Author

Jean-François Alcover, Jul 17 2014

Keywords

• nonn
• cons
• easy

Comments

See A245198.

Examples

			1.1166459711038098826457154510731531789665120066974040164563421606...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

• Eric Weisstein's MathWorld, Landau-Kolmogorov Constants
• Eric Weisstein's MathWorld, Favard Constants

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

Mathematica

a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[5,2], 10, 101] // First

Formula

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).

C(5,2) = (5*5^(4/5))/(8*2^(4/5)*3^(1/5)) = (1953125/1572864)^(1/5).