OFFSET
1,3
COMMENTS
By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 14 2019
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
REFERENCES
S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Hyperbolic Sine
Eric Weisstein's World of Mathematics, Hyperbolic Functions
Eric Weisstein's World of Mathematics, Factorial Sums
FORMULA
Equals (e - e^(-1))/2.
Equals sin(i)/i. - N. J. A. Sloane, Feb 12 2010
Equals Sum_{n>=0} 1/A009445(n). See Gradsteyn-Ryzhik (0.245.6.) - R. J. Mathar, Oct 27 2012
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
Equals Product_{k>=1} 1 + 1/(k * Pi)^2. - Amiram Eldar, Jul 16 2020
EXAMPLE
1.17520119364380145688238185059...
MATHEMATICA
First@ RealDigits@ N[Sinh@ 1, 120] (* Michael De Vlieger, Sep 04 2016 *)
PROG
(PARI) sinh(1)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Aug 07 2002
STATUS
approved