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 A073742 #56 Feb 16 2025 08:32:46
%S A073742 1,1,7,5,2,0,1,1,9,3,6,4,3,8,0,1,4,5,6,8,8,2,3,8,1,8,5,0,5,9,5,6,0,0,
%T A073742 8,1,5,1,5,5,7,1,7,9,8,1,3,3,4,0,9,5,8,7,0,2,2,9,5,6,5,4,1,3,0,1,3,3,
%U A073742 0,7,5,6,7,3,0,4,3,2,3,8,9,5,6,0,7,1,1,7,4,5,2,0,8,9,6,2,3,3,9,1,8,4,0,4,1
%N A073742 Decimal expansion of sinh(1).
%C A073742 By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 14 2019
%C A073742 Decimal expansion of u > 0 such that 1 = arclength on the hyperbola y^2 - x^2 = 1 from (0,0) to (u,y(u)). - _Clark Kimberling_, Jul 04 2020
%D A073742 S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
%D A073742 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 2, equation 2:5:7 at page 20.
%H A073742 G. C. Greubel, <a href="/A073742/b073742.txt">Table of n, a(n) for n = 1..5000</a>
%H A073742 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicSine.html">Hyperbolic Sine</a>.
%H A073742 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicFunctions.html">Hyperbolic Functions</a>.
%H A073742 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FactorialSums.html">Factorial Sums</a>.
%H A073742 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A073742 Equals (e - e^(-1))/2.
%F A073742 Equals sin(i)/i. - _N. J. A. Sloane_, Feb 12 2010
%F A073742 Equals Sum_{n>=0} 1/A009445(n). See Gradsteyn-Ryzhik (0.245.6.) - _R. J. Mathar_, Oct 27 2012
%F A073742 Continued fraction representation: sinh(1) = 1 + 1/(6 - 6/(21 - 20/(43 - 42/(73 - ... - (2*n - 1)*(2*n - 2)/((2*n*(2*n + 1) + 1) - ... ))))). See A051397 for proof. Cf. A049469. - _Peter Bala_, Sep 02 2016
%F A073742 Equals Product_{k>=1} 1 + 1/(k * Pi)^2. - _Amiram Eldar_, Jul 16 2020
%F A073742 Equals 1/A073745 = A174548/2. - _Hugo Pfoertner_, Dec 27 2024
%e A073742 1.17520119364380145688238185059...
%t A073742 First@ RealDigits@ N[Sinh@ 1, 120] (* _Michael De Vlieger_, Sep 04 2016 *)
%o A073742 (PARI) sinh(1)
%Y A073742 Cf. A068139 (continued fraction), A073743, A073744, A073745, A073746, A073747, A049469, A049470, A174548.
%K A073742 cons,nonn
%O A073742 1,3
%A A073742 _Rick L. Shepherd_, Aug 07 2002