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

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, 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, 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

Offset: 1

Author

Jean-François Alcover, Jul 17 2014

Keywords

• nonn
• cons
• easy

Comments

Decimal expansion of the Landau-Kolmogorov constant C(4,2) for derivatives in the case L_infinity(infinity, infinity).

See A245198.

Apart from the first digit the same as A176057. - R. J. Mathar, Jul 21 2014

Examples

			1.095445115010332226913939565601604267905489389995966508453788899464986554...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
• Eric Weisstein's MathWorld, Landau-Kolmogorov Constants.
• Eric Weisstein's MathWorld, Favard Constants.

Crossrefs

Cf. A050970, A050971, A244091, A245198.

Programs

Mathematica

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
RealDigits[Sqrt[6/5], 10, 100][[1]] (* Amiram Eldar, Jul 19 2022 *)

PARI

sqrt(6/5) \\ Charles R Greathouse IV, Aug 26 2017

Formula

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).

C(4,2) = sqrt(6/5).

Equals Sum_{k>=0} binomial(2*k,k)/24^k. - Amiram Eldar, Jul 19 2022