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A073742
Decimal expansion of sinh(1).
40
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, 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, 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
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
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
Cf. A068139 (continued fraction), A073745 (csch(1)=1/A073742), A073743 (cosh(1)), A073744 (tanh(1)), A073746 (sech(1)), A073747 (coth(1)), A049469 (sin(1)), A049470 (cos(1)).
Sequence in context: A216853 A272169 A084911 * A071876 A306538 A191503
KEYWORD
cons,nonn
AUTHOR
Rick L. Shepherd, Aug 07 2002
STATUS
approved