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 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 (list; constant; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..99. 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 Adjacent sequences: A240904 A240905 A240906 * A240908 A240909 A240910 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Apr 14 2014 STATUS approved

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Last modified September 12 20:35 EDT 2024. Contains 375854 sequences. (Running on oeis4.)