A263809 Decimal expansion of C_{1/2}, a constant related to Kolmogorov's inequalities.

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, 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, 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

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..105.

Burgess Davis, On Kolmogorov's Inequalities, Transactions of the American Mathematical Society Vol. 222 (Sep., 1976), pp. 179-192.

Formula

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

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

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

Example

2.78640785937135371836849252065073648531496243503123575794856326376...

Mathematica

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

Prog

(PARI) gamma(1/4)^2/(Pi*gamma(3/4)^2) \\ Michel Marcus, Oct 27 2015

Crossrefs

Cf. A068465, A068466, A093341, A242822.

Sequence in context: A352495 A141721 A129603 * A102268 A378942 A155062

Adjacent sequences: A263806 A263807 A263808 * A263810 A263811 A263812

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 27 2015

Status

approved