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%I #5 Jul 17 2014 22:09:49
%S 1,0,4,4,2,5,7,9,0,9,3,0,9,7,9,5,1,4,3,4,4,5,3,6,9,6,1,7,1,5,5,7,0,2,
%T 5,8,3,0,8,0,4,2,0,8,0,4,2,0,2,5,3,7,2,0,7,7,5,7,6,1,3,4,1,5,8,0,0,2,
%U 3,2,5,8,8,8,0,0,6,2,3,5,7,8,8,7,4,4,6,0,2,0,1,1,1,9,2,2,0,2,7,8,5,4,7,2,4
%N Decimal expansion of the Landau-Kolmogorov constant C(5,1) 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(5,1) = (5*5^(4/5))/(8*2^(4/5)*3^(1/5)) = (1953125/1572864)^(1/5).
%e 1.0442579093097951434453696171557025830804208042025372077576134158002325888...
%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[5,1], 10, 105] // First
%Y Cf. A050970, A050971, A244091, A245198.
%K nonn,cons,easy
%O 1,3
%A _Jean-François Alcover_, Jul 17 2014
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