A263809 - OEIS

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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

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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.