A377405 - OEIS

%I #18 Nov 01 2024 03:52:40

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

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

%U 0,5,7,4,8,3,9,5,3,7,4,5,6,6,1,3,9,0,1,9,3,8,9,7,1,3,4,8,3,3,0,7

%N Decimal expansion of Pi*csc(Pi/5).

%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 33.

%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 360.

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

%F Equals Gamma(1/5)*Gamma(4/5) = 2*Pi*sqrt(5)*sqrt(2+phi)/5 (see Finch).

%F Equals Integral_{x=0..oo} log(1 + x^(-5)) dx (see Shamos).

%F Equals sqrt(2*(1 + 1/sqrt(5)))*Pi.

%F Equals 10 * Sum_{n>=1} (-1)^(n+1)/A345019(n). - _Amiram Eldar_, Oct 27 2024

%F Equals 5*A352324. - _Hugo Pfoertner_, Oct 28 2024

%e 5.344796660577975567125921862534413199507254626...

%t RealDigits[Pi*Csc[Pi/5],10,100][[1]]

%Y Cf. A000796, A001622, A002163, A010476, A019692, A175380, A345019, A340722, A352324.

%K nonn,cons

%O 1,1

%A _Stefano Spezia_, Oct 27 2024