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

%I A245293 #6 Feb 16 2025 08:33:23
%S A245293 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,
%T A245293 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,
%U A245293 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
%N A245293 Decimal expansion of the Landau-Kolmogorov constant C(4,1) for derivatives in the case L_infinity(infinity, infinity).
%C A245293 See A245198.
%D A245293 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.
%H A245293 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>
%H A245293 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/FavardConstants.html">Favard Constants</a>
%F A245293 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 A245293 C(4,1) = 4*(2/3)^(1/4)/5^(3/4) = (512/375)^(1/4).
%e A245293 1.0809601238456275151880801506365456492375770747255234380135664425927599...
%t A245293 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
%Y A245293 Cf. A050970, A050971, A244091, A245198.
%K A245293 nonn,cons,easy
%O A245293 1,3
%A A245293 _Jean-François Alcover_, Jul 17 2014