A263809 - OEIS

%I #7 Oct 27 2015 07:33:52

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

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

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

%N Decimal expansion of C_{1/2}, a constant related to Kolmogorov's inequalities.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.7 Riesz-Kolmogorov Constants, p. 474.

%H Burgess Davis, <a href="http://dx.doi.org/10.2307/1997664">On Kolmogorov's Inequalities</a>, Transactions of the American Mathematical Society Vol. 222 (Sep., 1976), pp. 179-192.

%F C_{1/2} = gamma(1/4)^2/(Pi*gamma(3/4)^2).

%F Equals (1/Pi^2)*(integral_{0..Pi} sqrt(csc(t)) dt)^2.

%F Also equals (8/Pi^2)*A093341^2.

%e 2.78640785937135371836849252065073648531496243503123575794856326376...

%t RealDigits[Gamma[1/4]^2/(Pi*Gamma[3/4]^2), 10, 105] // First

%o (PARI) gamma(1/4)^2/(Pi*gamma(3/4)^2) \\ _Michel Marcus_, Oct 27 2015

%Y Cf. A068465, A068466, A093341, A242822.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Oct 27 2015