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A245294 Decimal expansion of the square root of 6/5.

%I A245294 #22 Feb 16 2025 08:33:23
%S A245294 1,0,9,5,4,4,5,1,1,5,0,1,0,3,3,2,2,2,6,9,1,3,9,3,9,5,6,5,6,0,1,6,0,4,
%T A245294 2,6,7,9,0,5,4,8,9,3,8,9,9,9,5,9,6,6,5,0,8,4,5,3,7,8,8,8,9,9,4,6,4,9,
%U A245294 8,6,5,5,4,2,4,5,4,4,5,4,6,7,6,0,1,7,1,6,8,7,2,3,2,7,7,4,1,2,5,1,5,2,9,4,5
%N A245294 Decimal expansion of the square root of 6/5.
%C A245294 Decimal expansion of the Landau-Kolmogorov constant C(4,2) for derivatives in the case L_infinity(infinity, infinity).
%C A245294 See A245198.
%C A245294 Apart from the first digit the same as A176057. - _R. J. Mathar_, Jul 21 2014
%D A245294 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.
%H A245294 Daniel Starodubtsev, <a href="/A245294/b245294.txt">Table of n, a(n) for n = 1..10000</a>
%H A245294 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Landau-KolmogorovConstants.html">Landau-Kolmogorov Constants</a>.
%H A245294 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/FavardConstants.html">Favard Constants</a>.
%F A245294 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 A245294 C(4,2) = sqrt(6/5).
%F A245294 Equals Sum_{k>=0} binomial(2*k,k)/24^k. - _Amiram Eldar_, Jul 19 2022
%e A245294 1.095445115010332226913939565601604267905489389995966508453788899464986554...
%t A245294 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, 2], 10, 105] // First
%t A245294 RealDigits[Sqrt[6/5], 10, 100][[1]] (* _Amiram Eldar_, Jul 19 2022 *)
%o A245294 (PARI) sqrt(6/5) \\ _Charles R Greathouse IV_, Aug 26 2017
%Y A245294 Cf. A050970, A050971, A244091, A245198.
%K A245294 nonn,cons,easy
%O A245294 1,3
%A A245294 _Jean-François Alcover_, Jul 17 2014