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A245299 Decimal expansion of the Landau-Kolmogorov constant C(5,4) for derivatives in the case L_infinity(-infinity, infinity). 0

%I

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

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

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

%N Decimal expansion of the Landau-Kolmogorov constant C(5,4) 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(5,4) = (15/2)^(1/5).

%e 1.49627786973884473850810213932978255331700624709325410308756863950368...

%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[5,4], 10, 105] // First

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

%K nonn,cons,easy

%O 1,2

%A _Jean-Fran├žois Alcover_, Jul 17 2014

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Last modified April 6 08:44 EDT 2020. Contains 333268 sequences. (Running on oeis4.)