A073742 Decimal expansion of sinh(1).

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

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

Index entries for transcendental numbers

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

Adjacent sequences: A073739 A073740 A073741 * A073743 A073744 A073745

Keyword

cons,nonn

Author

Rick L. Shepherd, Aug 07 2002

Status

approved