A073447 Decimal expansion of csc(1).

1, 1, 8, 8, 3, 9, 5, 1, 0, 5, 7, 7, 8, 1, 2, 1, 2, 1, 6, 2, 6, 1, 5, 9, 9, 4, 5, 2, 3, 7, 4, 5, 5, 1, 0, 0, 3, 5, 2, 7, 8, 2, 9, 8, 3, 4, 0, 9, 7, 9, 6, 2, 6, 2, 5, 2, 6, 5, 2, 5, 3, 6, 6, 6, 3, 5, 9, 1, 8, 4, 3, 6, 7, 3, 5, 7, 1, 9, 0, 4, 8, 7, 9, 1, 3, 6, 6, 3, 5, 6, 8, 0, 3, 0, 8, 5, 3, 0, 2, 3, 2, 4, 7, 2, 4

Offset: 1

Author

Rick L. Shepherd, Aug 01 2002

Keywords

• cons
• nonn

Comments

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

Examples

			1.18839510577812121626159945237...
		

Links

• Mohammad K. Azarian, Solution of Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395. Solution published in Vol. 37 , No. 5, November 2006, pp. 394-395.
• Index entries for transcendental numbers.

Crossrefs

Cf. A049469 (sin(1)=1/A073447), A049470 (cos(1)), A049471 (tan(1)), A073448 (sec(1)), A073449 (cot(1)).

Cf. A027641, A027642.

Programs

Mathematica

RealDigits[Csc[1], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

PARI

1/sin(1)

Formula

Equals Sum_{n=-oo..oo} ((-1)^n/(1 + n*Pi)). - Jean-François Alcover, Mar 21 2013.

Equals Sum_{k>=0} (-1)^k * (2 - 4^k) * bernoulli(2*k)/(2*k)! = Sum_{k>=0} (-1)^k * (2 - 4^k) * A027641(2*k)/(A027642(2*k)*(2*k)!). - Amiram Eldar, Aug 03 2020