A245297 - OEIS

%I #6 Feb 16 2025 08:33:23

%S 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,

%T 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,

%U 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

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

%C See A245198.

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

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>

%H Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/FavardConstants.html">Favard Constants</a>

%F 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).

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

%e 1.1166459711038098826457154510731531789665120066974040164563421606...

%t 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

%Y Cf. A050970, A050971, A244091, A245198.

%K nonn,cons,easy

%O 1,4

%A _Jean-François Alcover_, Jul 17 2014