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A073744 Decimal expansion of tanh(1).

%I A073744 #31 Feb 16 2025 08:32:46
%S A073744 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,
%T A073744 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,
%U A073744 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
%N A073744 Decimal expansion of tanh(1).
%C A073744 Also decimal expansion of tan(i)/i. - _N. J. A. Sloane_, Feb 12 2010
%C A073744 tanh(x) = (e^x - e^(-x)) / (e^x + e^(-x)).
%C A073744 By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 14 2019
%D A073744 S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
%H A073744 Ivan Panchenko, <a href="/A073744/b073744.txt">Table of n, a(n) for n = 0..1000</a>
%H A073744 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicTangent.html">Hyperbolic Tangent</a>
%H A073744 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicFunctions.html">Hyperbolic Functions</a>
%H A073744 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A073744 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
%F A073744 Equal to the continued fraction [0;1,3,5,...,2n-1,...]. - _Thomas Ordowski_, Oct 22 2024
%F A073744 Equals 1-A349003. - _Hugo Pfoertner_, Oct 22 2024
%e A073744 0.76159415595576488811945828260...
%t A073744 RealDigits[Tanh[1], 10, 100][[1]] (* _Amiram Eldar_, Aug 19 2020 *)
%o A073744 (PARI) tanh(1)
%Y A073744 Cf. A004273 (continued fraction), A073747 (coth(1)=1/A073744), A073742 (sinh(1)), A073743 (cosh(1)), A073745 (csch(1)), A073746 (sech(1)).
%Y A073744 Cf. A027641, A027642, A349003.
%K A073744 cons,nonn
%O A073744 0,1
%A A073744 _Rick L. Shepherd_, Aug 07 2002