A246856 Decimal expansion of 'alpha', the threshold angle associated with the best constant in [a variation of] Hardy's inequality for a domain defined as a non-convex plane sector of angle alpha.
4, 8, 5, 6, 0, 5, 5, 3, 2, 0, 9, 3, 1, 6, 6, 2, 0, 3, 8, 6, 2, 6, 4, 3, 5, 3, 4, 8, 9, 0, 5, 2, 9, 3, 9, 8, 5, 5, 1, 9, 5, 3, 7, 8, 3, 1, 0, 2, 0, 8, 8, 0, 2, 5, 8, 3, 8, 3, 4, 6, 2, 1, 2, 4, 3, 6, 0, 6, 2, 2, 7, 9, 0, 2, 3, 6, 5, 5, 0, 5, 9, 2, 8, 0, 6, 9, 8, 2, 6, 2, 7, 2, 6, 5, 7, 8, 9, 6, 2, 4, 2, 9
Offset: 1
Examples
4.85605532093166203862643534890529398551953783102088...
Links
- Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 30.
Programs
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Mathematica
alpha = Pi + 4*ArcTan[4*Gamma[3/4]^2/Gamma[1/4]^2]; RealDigits[alpha, 10, 102] // First
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PARI
Pi + 4*atan(4*gamma(3/4)^2/gamma(1/4)^2) \\ Michel Marcus, Sep 05 2014
Formula
alpha = Pi + 4*arctan(4*Gamma(3/4)^2/Gamma(1/4)^2).