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

Author

Jean-François Alcover, Oct 27 2015

Keywords

• nonn
• cons
• easy

Examples

			2.78640785937135371836849252065073648531496243503123575794856326376...
		

References

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

Links

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

Crossrefs

Cf. A068465, A068466, A093341, A242822.

Programs

Mathematica

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

PARI

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

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.