

A049470


Decimal expansion of cos(1).


37



5, 4, 0, 3, 0, 2, 3, 0, 5, 8, 6, 8, 1, 3, 9, 7, 1, 7, 4, 0, 0, 9, 3, 6, 6, 0, 7, 4, 4, 2, 9, 7, 6, 6, 0, 3, 7, 3, 2, 3, 1, 0, 4, 2, 0, 6, 1, 7, 9, 2, 2, 2, 2, 7, 6, 7, 0, 0, 9, 7, 2, 5, 5, 3, 8, 1, 1, 0, 0, 3, 9, 4, 7, 7, 4, 4, 7, 1, 7, 6, 4, 5, 1, 7, 9, 5, 1, 8, 5, 6, 0, 8, 7, 1, 8, 3, 0, 8, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

Also, decimal expansion of the real part of e^i.  Bruno Berselli, Feb 08 2013
By the LindemannWeierstrass theorem, this constant is transcendental.  Charles R Greathouse IV, May 13 2019


LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..2000
Mohammad K. Azarian, FortyFive Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413414.
Mohammad K. Azarian, Solution of FortyFive Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394395.
I. S. Gradsteyn, I. M. Ryzhik, Table of integrals, series and products, (1980), page 10 (formula 0.245.7).
Simon Plouffe, cos(1)
Eric Weisstein's World of Mathematics, Factorial Sums
Index entries for transcendental numbers


FORMULA

Continued fraction representation: cos(1) = 1/(1 + 1/(1 + 2/(11 + 12/(29 + ... + (2*n  2)*(2*n  3)/((4*n^2  2*n  1) + ... ))))). See A275651 for proof. Cf. A073743.  Peter Bala, Sep 02 2016
Equals Sum_{k >= 0} (1)^k/A010050(k), where A010050(k) = (2k)! [See Gradshteyn and Ryzhik].  A.H.M. Smeets, Sep 22 2018


EXAMPLE

0.5403023058681397...


MAPLE

evalf(cos(1)); # Altug Alkan, Sep 22 2018


MATHEMATICA

RealDigits[Cos[1], 10, 110] [[1]]


PROG

(PARI) cos(1) \\ Charles R Greathouse IV, Jan 04 2016


CROSSREFS

Cf. A049469 (imaginary part of e^i), A211883 (real part of (i^e)), A211884 (imaginary part of (i^e)).  Bruno Berselli, Feb 08 2013
Cf. A073743 ( cosh(1) ), A275651.
Sequence in context: A159799 A185579 A197134 * A309699 A153106 A021189
Adjacent sequences: A049467 A049468 A049469 * A049471 A049472 A049473


KEYWORD

cons,easy,nonn


AUTHOR

Albert du Toit (dutwa(AT)intekom.co.za), N. J. A. Sloane


STATUS

approved



