A240907 Decimal expansion of Hopf's constant.

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

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