A245293 Decimal expansion of the Landau-Kolmogorov constant C(4,1) for derivatives in the case L_infinity(infinity, infinity).

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

Offset: 1

Author

Jean-François Alcover, Jul 17 2014

Keywords

• nonn
• cons
• easy

Comments

See A245198.

Examples

			1.0809601238456275151880801506365456492375770747255234380135664425927599...
		

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[4, 1], 10, 105] // 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(4,1) = 4*(2/3)^(1/4)/5^(3/4) = (512/375)^(1/4).