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

Author

Rick L. Shepherd, Aug 07 2002

Keywords

• cons
• nonn

Comments

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

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

Examples

			0.85091812823932154513384276328...
		

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

Crossrefs

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

Programs

Mathematica

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

PARI

1/sinh(1)

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