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

0,1

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

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

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

Example

0.76159415595576488811945828260...

Mathematica

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

Prog

(PARI) tanh(1)

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.

Sequence in context: A319331 A371804 A010511 * A112253 A347074 A112252

Adjacent sequences: A073741 A073742 A073743 * A073745 A073746 A073747

Keyword

cons,nonn

Author

Rick L. Shepherd, Aug 07 2002

Status

approved