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

1,1

Links

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 30.

Formula

alpha = Pi + 4*arctan(4*Gamma(3/4)^2/Gamma(1/4)^2).

Example

4.85605532093166203862643534890529398551953783102088...

Mathematica

alpha = Pi + 4*ArcTan[4*Gamma[3/4]^2/Gamma[1/4]^2]; RealDigits[alpha, 10, 102] // First

Prog

(PARI) Pi + 4*atan(4*gamma(3/4)^2/gamma(1/4)^2) \\ Michel Marcus, Sep 05 2014

Crossrefs

Cf. A068465, A068466.

Sequence in context: A021210 A197849 A292466 * A388159 A113969 A155782

Adjacent sequences: A246853 A246854 A246855 * A246857 A246858 A246859

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 05 2014

Status

approved