A073745 Decimal expansion of csch(1).

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

Offset

0,1

Comments

csch(x) = 2/(e^x - e^(-x)).

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

References

Samuel M. Selby (ed.), 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 Cosecant.

Eric Weisstein's World of Mathematics, Hyperbolic Functions.

Index entries for transcendental numbers

Formula

Equals Sum_{k>=0} B(2*k) * (2 - 2^(2*k)) / (2*k)!, where B(k) is the k-th Bernoulli number. - Amiram Eldar, May 15 2021

Example

0.85091812823932154513384276328...

Mathematica

RealDigits[Csch[1], 10, 100][[1]] (* Amiram Eldar, May 15 2021 *)

Prog

(PARI) 1/sinh(1)

Crossrefs

Cf. A068139 (continued fraction), A073742 (sinh(1)=1/A073745), A073743 (cosh(1)), A073744 (tanh(1)), A073746 (sech(1)), A073747 (coth(1)).

Sequence in context: A197841 A143347 A073448 * A086730 A249449 A357466

Adjacent sequences: A073742 A073743 A073744 * A073746 A073747 A073748

Keyword

cons,nonn

Author

Rick L. Shepherd, Aug 07 2002

Status

approved