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A073447 Decimal expansion of csc(1). 14

%I #29 May 29 2023 01:48:20

%S 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,

%T 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,

%U 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

%N Decimal expansion of csc(1).

%C By the Lindemann-Weierstrass theorem, this constant is transcendental. - _Charles R Greathouse IV_, May 13 2019

%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/27646393">Solution of Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813</a>, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395. <a href="http://www.jstor.org/stable/27646393">Solution</a> published in Vol. 37 , No. 5, November 2006, pp. 394-395.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals Sum_{n=-oo..oo} ((-1)^n/(1 + n*Pi)). - _Jean-François Alcover_, Mar 21 2013.

%F 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

%e 1.18839510577812121626159945237...

%t RealDigits[Csc[1], 10, 120][[1]] (* _Amiram Eldar_, May 29 2023 *)

%o (PARI) 1/sin(1)

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

%Y Cf. A027641, A027642.

%K cons,nonn

%O 1,3

%A _Rick L. Shepherd_, Aug 01 2002

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)