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A263809
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Decimal expansion of C_{1/2}, a constant related to Kolmogorov's inequalities.
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1
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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
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.7 Riesz-Kolmogorov Constants, p. 474.
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LINKS
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FORMULA
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C_{1/2} = gamma(1/4)^2/(Pi*gamma(3/4)^2).
Equals (1/Pi^2)*(integral_{0..Pi} sqrt(csc(t)) dt)^2.
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EXAMPLE
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2.78640785937135371836849252065073648531496243503123575794856326376...
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MATHEMATICA
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RealDigits[Gamma[1/4]^2/(Pi*Gamma[3/4]^2), 10, 105] // First
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PROG
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(PARI) gamma(1/4)^2/(Pi*gamma(3/4)^2) \\ _Michel Marcus_, Oct 27 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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_Jean-François Alcover_, Oct 27 2015
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STATUS
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approved
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