A133867 Decimal expansion of the smallest positive fixed point of csch(x) (and csch^-1(x)).

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, 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, 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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..104.

Mohammad K. Azarian, On the Fixed Points of a Function and the Fixed Points of its Composite Functions, 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.

Mohammad K. Azarian, Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal, Vol. 38, No. 1, January 2007, p. 60.

Mohammad K. Azarian, Solution to Fixed Points of a Quadratic Polynomial, Problem 841, College Mathematics Journal Vol. 39, No. 1, January 2008, pp. 66-67.

Eric Weisstein's World of Mathematics, Hyperbolic Cosecant.

Eric Weisstein's World of Mathematics, Fixed Point.

Example

0.93202002935234390539...

Mathematica

RealDigits[x /. FindRoot[Csch[x] == x, {x, 1}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, May 25 2023 *)

Crossrefs

Cf. A009341.

Sequence in context: A199152 A306808 A086232 * A210113 A195704 A176516

Adjacent sequences: A133864 A133865 A133866 * A133868 A133869 A133870

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 27 2007

Status

approved