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%I #13 Apr 16 2021 04:20:24
%S 7,1,0,4,4,6,0,8,9,5,9,8,7,6,3,0,7,2,7,3,2,5,2,4,1,4,1,6,9,9,1,5,3,6,
%T 7,1,9,9,3,2,0,1,3,3,3,9,5,8,7,8,5,2,3,9,0,9,2,7,9,7,9,6,8,5,1,0,9,7,
%U 2,6,9,7,0,4,3,9,1,5,7,6,8,1,5,2,7,6,3,6,3,9,9,8,0,9,0,7,7,5,2,8
%N Decimal expansion of Hopf's constant.
%C Named after the German-American mathematician and astronomer Eberhard Hopf (1902-1983). - _Amiram Eldar_, Apr 16 2021
%D Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 345.
%H Steven Finch, <a href="/A240907/a240907.pdf">Radiative Transfer Equations</a>, December 30, 2008. [Cached copy, with permission of the author]
%H Eberhard Hopf, <a href="https://archive.org/details/mathematicalprob029085mbp">Mathematical Problems of Radiative Equilibrium</a>, Cambridge University Press, 1934.
%F 6/Pi^2 + 1/Pi * integral_{t=0..Pi/2} 3/t^2-1/(1-t*cot(t)) dt.
%e 0.710446089598763...
%p h:= 6/Pi^2 +1/Pi* int(3/t^2 -1/(1-t*cot(t)), t=0..Pi/2):
%p seq(parse(d), d=convert(evalf(h, 140), string)[2..120]); # _Alois P. Heinz_, Apr 14 2014
%t 6/Pi^2 + 1/Pi*NIntegrate[3/t^2 - 1/(1 - t*Cot[t]), {t, 0, Pi/2}, WorkingPrecision -> 100] // RealDigits[#, 10, 100]& // First
%K nonn,cons
%O 0,1
%A _Jean-François Alcover_, Apr 14 2014