A245298 - OEIS

%I #5 Jul 17 2014 22:10:12

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

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

%U 4,2,2,9,2,2,9,6,9,0,4,5,1,5,2,5,2,6,2,8,6,5,9,6,1,3,0,8,5,2,2,9,2,9,5,2

%N Decimal expansion of the Landau-Kolmogorov constant C(5,3) 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="http://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>

%H Eric Weisstein's MathWorld, <a href="http://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(5,3) = (1/2)*(15/2)^(2/5).

%e 1.11942373173510761162971108208126104124998556705860708652098279913...

%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[5,3], 10, 104] // First

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

%K nonn,cons,easy

%O 1,4

%A _Jean-François Alcover_, Jul 17 2014