This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A073743 #53 Feb 16 2025 08:32:46
%S A073743 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 A073743 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 A073743 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 A073743 Decimal expansion of cosh(1).
%C A073743 Also decimal expansion of cos(i). - _N. J. A. Sloane_, Feb 12 2010
%C A073743 cosh(x) = (e^x + e^(-x))/2.
%C A073743 Equals Sum_{n>=0} 1/A010050(n). See Gradsteyn-Ryzhik (0.245.5). - _R. J. Mathar_, Oct 27 2012
%C A073743 By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 14 2019
%D A073743 S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
%D A073743 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 2, equation 2:5:6 at page 20.
%H A073743 Ivan Panchenko, <a href="/A073743/b073743.txt">Table of n, a(n) for n = 1..1000</a>
%H A073743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicCosine.html">Hyperbolic Cosine</a>.
%H A073743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicFunctions.html">Hyperbolic Functions</a>.
%H A073743 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FactorialSums.html">Factorial Sums</a>.
%H A073743 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A073743 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 A073743 Equals Product_{k>=0} 1 + 4/((2*k+1)*Pi)^2. - _Amiram Eldar_, Jul 16 2020
%F A073743 Equals 1/A073746 = A137204/2. - _Hugo Pfoertner_, Dec 27 2024
%e A073743 1.54308063481524377847790562075...
%p A073743 Digits:=100: evalf(cosh(1)); # _Wesley Ivan Hurt_, Nov 18 2014
%t A073743 RealDigits[Cosh[1],10,120][[1]] (* _Harvey P. Dale_, Aug 03 2014 *)
%o A073743 (PARI) cosh(1)
%Y A073743 Cf. A068118 (continued fraction), A073742, A073744, A073745, A073746, A073747, A049470, A137204.
%K A073743 cons,nonn
%O A073743 1,2
%A A073743 _Rick L. Shepherd_, Aug 07 2002