A073743 Decimal expansion of cosh(1).

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, 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, 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

Offset

1,2

Comments

Also decimal expansion of cos(i). - N. J. A. Sloane, Feb 12 2010

cosh(x) = (e^x + e^(-x))/2.

Equals Sum_{n>=0} 1/A010050(n). See Gradsteyn-Ryzhik (0.245.5). - R. J. Mathar, Oct 27 2012

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 14 2019

References

S. Selby, editor, CRC Basic Mathematical Tables, CRC Press, 1970, p. 218.

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Hyperbolic Cosine

Eric Weisstein's World of Mathematics, Hyperbolic Functions

Eric Weisstein's World of Mathematics, Factorial Sums

Index entries for transcendental numbers

Formula

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

Equals Product_{k>=0} 1 + 4/((2*k+1)*Pi)^2. - Amiram Eldar, Jul 16 2020

Example

1.54308063481524377847790562075...

Maple

Digits:=100: evalf(cosh(1)); # Wesley Ivan Hurt, Nov 18 2014

Mathematica

RealDigits[Cosh[1], 10, 120][[1]] (* Harvey P. Dale, Aug 03 2014 *)

Prog

(PARI) cosh(1)

Crossrefs

Cf. A068118 (continued fraction), A073746 (sech(1)=1/A073743), A073742 (sinh(1)), A073744 (tanh(1)), A073745 (csch(1)), A073747 (coth(1)), A049470 (cos(1)).

Sequence in context: A019712 A020799 A199432 * A021652 A360778 A022961

Adjacent sequences: A073740 A073741 A073742 * A073744 A073745 A073746

Keyword

cons,nonn

Author

Rick L. Shepherd, Aug 07 2002

Status

approved