|
%I #20 May 15 2021 03:54:10
%S 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,
%T 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,
%U 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
%N Decimal expansion of csch(1).
%C csch(x) = 2/(e^x - e^(-x)).
%C By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 14 2019
%D Samuel M. Selby (ed.), CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
%H Ivan Panchenko, <a href="/A073745/b073745.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicCosecant.html">Hyperbolic Cosecant</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicFunctions.html">Hyperbolic Functions</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F 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
%e 0.85091812823932154513384276328...
%t RealDigits[Csch[1], 10, 100][[1]] (* _Amiram Eldar_, May 15 2021 *)
%o (PARI) 1/sinh(1)
%Y Cf. A068139 (continued fraction), A073742 (sinh(1)=1/A073745), A073743 (cosh(1)), A073744 (tanh(1)), A073746 (sech(1)), A073747 (coth(1)).
%K cons,nonn
%O 0,1
%A _Rick L. Shepherd_, Aug 07 2002
|
