A073744 Decimal expansion of tanh(1).

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

Offset: 0

Author

Rick L. Shepherd, Aug 07 2002

Keywords

• cons
• nonn

Comments

Also decimal expansion of tan(i)/i. - N. J. A. Sloane, Feb 12 2010

tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x)).

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

Examples

			0.76159415595576488811945828260...
		

References

• S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Hyperbolic Tangent
• Eric Weisstein's World of Mathematics, Hyperbolic Functions
• Index entries for transcendental numbers

Crossrefs

Cf. A004273 (continued fraction), A073747 (coth(1)=1/A073744), A073742 (sinh(1)), A073743 (cosh(1)), A073745 (csch(1)), A073746 (sech(1)).

Cf. A027641, A027642, A349003.

Programs

Mathematica

RealDigits[Tanh[1], 10, 100][[1]] (* Amiram Eldar, Aug 19 2020 *)

PARI

tanh(1)

Formula

Equals Sum_{k>=1} bernoulli(2*k)*2^(2*k)*(2^(2*k)-1)/(2*k)!, where bernoulli(k) = A027641(k)/A027642(k) is the k-th Bernoulli number. - Amiram Eldar, Aug 19 2020

Equal to the continued fraction [0;1,3,5,...,2n-1,...]. - Thomas Ordowski, Oct 22 2024

Equals 1-A349003. - Hugo Pfoertner, Oct 22 2024