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

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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 A155062 A021786

Adjacent sequences: A263806 A263807 A263808 * A263810 A263811 A263812

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 27 2015

Status

approved