A073743 - OEIS

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

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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.

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 2, equation 2:5:6 at page 20.

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

Equals 1/A073746 = A137204/2. - Hugo Pfoertner, Dec 27 2024

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), A073742, A073744, A073745, A073746, A073747, A049470, A137204.