login
A240907
Decimal expansion of Hopf's constant.
1
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, 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, 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
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
Sequence in context: A218620 A195911 A231096 * A179376 A152447 A198611
KEYWORD
nonn,cons
AUTHOR
STATUS
approved