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%I #36 Sep 15 2022 10:12:01
%S 1,5,4,3,0,8,0,6,3,4,8,1,5,2,4,3,7,7,8,4,7,7,9,0,5,6,2,0,7,5,7,0,6,1,
%T 6,8,2,6,0,1,5,2,9,1,1,2,3,6,5,8,6,3,7,0,4,7,3,7,4,0,2,2,1,4,7,1,0,7,
%U 6,9,0,6,3,0,4,9,2,2,3,6,9,8,9,6,4,2,6,4,7,2,6,4,3,5,5,4,3,0,3,5,5,8,7,0,4
%N Decimal expansion of cosh(1).
%C Also decimal expansion of cos(i). - _N. J. A. Sloane_, Feb 12 2010
%C cosh(x) = (e^x + e^(-x))/2.
%C Equals Sum_{n>=0} 1/A010050(n). See Gradsteyn-Ryzhik (0.245.5). - _R. J. Mathar_, Oct 27 2012
%C By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 14 2019
%D S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
%H Ivan Panchenko, <a href="/A073743/b073743.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicCosine.html">Hyperbolic Cosine</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HyperbolicFunctions.html">Hyperbolic Functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FactorialSums.html">Factorial Sums</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Continued fraction representation: cosh(1) = 1 + 1/(2 - 2/(13 - 12/(31 - ... - (2*n - 4)*(2*n - 5)/((4*n^2 - 10*n + 7) - ... )))). See A051396 for proof. Cf. A049470 (cos(1)) and A073742 (sinh(1)). - _Peter Bala_, Sep 05 2016
%F Equals Product_{k>=0} 1 + 4/((2*k+1)*Pi)^2. - _Amiram Eldar_, Jul 16 2020
%e 1.54308063481524377847790562075...
%p Digits:=100: evalf(cosh(1)); # _Wesley Ivan Hurt_, Nov 18 2014
%t RealDigits[Cosh[1],10,120][[1]] (* _Harvey P. Dale_, Aug 03 2014 *)
%o (PARI) cosh(1)
%Y Cf. A068118 (continued fraction), A073746 (sech(1)=1/A073743), A073742 (sinh(1)), A073744 (tanh(1)), A073745 (csch(1)), A073747 (coth(1)), A049470 (cos(1)).
%K cons,nonn
%O 1,2
%A _Rick L. Shepherd_, Aug 07 2002
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