OFFSET
0,1
COMMENTS
Named after the German-American mathematician and astronomer Eberhard Hopf (1902-1983). - Amiram Eldar, Apr 16 2021
REFERENCES
Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 345.
LINKS
Steven Finch, Radiative Transfer Equations, December 30, 2008. [Cached copy, with permission of the author]
Eberhard Hopf, Mathematical Problems of Radiative Equilibrium, Cambridge University Press, 1934.
FORMULA
6/Pi^2 + 1/Pi * integral_{t=0..Pi/2} 3/t^2-1/(1-t*cot(t)) dt.
EXAMPLE
0.710446089598763...
MAPLE
h:= 6/Pi^2 +1/Pi* int(3/t^2 -1/(1-t*cot(t)), t=0..Pi/2):
seq(parse(d), d=convert(evalf(h, 140), string)[2..120]); # Alois P. Heinz, Apr 14 2014
MATHEMATICA
6/Pi^2 + 1/Pi*NIntegrate[3/t^2 - 1/(1 - t*Cot[t]), {t, 0, Pi/2}, WorkingPrecision -> 100] // RealDigits[#, 10, 100]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Apr 14 2014
STATUS
approved