login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Decimal expansion of the smallest positive fixed point of csch(x) (and csch^-1(x)).
2

%I #21 Dec 01 2024 11:37:33

%S 9,3,2,0,2,0,0,2,9,3,5,2,3,4,3,9,0,5,3,9,1,1,1,4,8,4,0,1,9,3,6,3,8,1,

%T 2,2,6,4,4,8,3,9,2,2,3,3,0,1,9,0,7,8,7,2,0,1,4,9,2,5,6,4,0,5,8,5,4,9,

%U 4,6,8,1,1,3,7,6,6,2,7,7,9,4,5,4,2,9,6,8,1,4,4,1,2,8,0,6,5,8,8,7,0,6,1,0,8

%N Decimal expansion of the smallest positive fixed point of csch(x) (and csch^-1(x)).

%C cosh(x) appears to be the positive solution for z in arccosh(z) = d/dz arcosh(z). - _Colin Linzer_, Nov 15 2024

%H Mohammad K. Azarian, <a href="http://www.ijpam.eu/contents/2008-46-1/3/3.pdf">On the Fixed Points of a Function and the Fixed Points of its Composite Functions</a>, International Journal of Pure and Applied Mathematics, Vol. 46, No. 1, 2008, pp. 37-44. Mathematical Reviews, MR2433713 (2009c:65129), March 2009. Zentralblatt MATH, Zbl 1160.65015.

%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/27646421">Fixed Points of a Quadratic Polynomial, Problem 841</a>, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60.

%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/27646572">Solution to Fixed Points of a Quadratic Polynomial, Problem 841</a>, College Mathematics Journal Vol. 39, No. 1, January 2008, pp. 66-67.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicCosecant.html">Hyperbolic Cosecant</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FixedPoint.html">Fixed Point</a>.

%e 0.93202002935234390539...

%t RealDigits[x /. FindRoot[Csch[x] == x, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, May 25 2023 *)

%Y Cf. A009341.

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Sep 27 2007