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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. 0

%I

%S 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,

%T 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,

%U 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

%N 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.

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf">Errata and Addenda to Mathematical Constants</a>, p. 30.

%H Steven R. Finch, <a href="/A002193/a002193.pdf">Errata and Addenda to Mathematical Constants</a>, January 22, 2016. [Cached copy, with permission of the author]

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

%e 4.85605532093166203862643534890529398551953783102088...

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

%o (PARI) Pi + 4*atan(4*gamma(3/4)^2/gamma(1/4)^2) \\ _Michel Marcus_, Sep 05 2014

%Y Cf. A068465, A068466.

%K nonn,cons,easy

%O 1,1

%A _Jean-Fran├žois Alcover_, Sep 05 2014

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Last modified September 16 10:46 EDT 2019. Contains 327094 sequences. (Running on oeis4.)