A307178 Decimal expansion of coth(1/2).

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

Offset: 1

Author

Terry D. Grant, Mar 27 2019

Keywords

• cons
• nonn

Comments

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 14 2019

Examples

			2.163953413738... = 2 + 1/(6 + 1/(10 + 1/(14 + 1/(18 + ...)))).
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A016825 (continued fraction), A073333, A073747 (coth(1)).

Cf. A000367, A002445.

Programs

Mathematica

RealDigits[Coth[1/2], 10, 120][[1]] (* or *) BesselI[-1/2, 1/2]/BesselI[1/2, 1/2]

PARI

cotanh(1/2) \\ Michel Marcus, Mar 28 2019

Formula

Equals (exp(1)+1)/(exp(1)-1).

Equals (BesselI(3/2,1/2)/BesselI(1/2,1/2))+2.

Equals BesselI(-1/2,1/2)/BesselI(1/2,1/2).

Equals 2 * Sum_{k>=0} B(2*k)/(2*k)!, where B(2*k) = A000367(k)/A002445(k) are the Bernoulli numbers. - Amiram Eldar, Nov 25 2020

Equals 2 * A073333 + 1. - Antonio Graciá Llorente, Jan 21 2024