OFFSET
1,3
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
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.
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
EXAMPLE
1.095445115010332226913939565601604267905489389995966508453788899464986554...
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 *)
PROG
(PARI) sqrt(6/5) \\ Charles R Greathouse IV, Aug 26 2017
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 17 2014
STATUS
approved