A175316 - OEIS

%I #16 Feb 16 2023 05:32:14

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

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

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

%N Decimal expansion of coth(Pi).

%F Equals A175314 divided by A175315.

%F Equals (exp(tau) + 1)/(exp(tau) - 1), where tau = 2*Pi = A019692. - _Peter Luschny_, May 22 2021

%F From _Wolfe Padawer_, Jan 28 2023: (Start)

%F Equals Sum_{k>=-oo} 1/(Pi + Pi*k^2).

%F Equals 1 + Sum_{k>=0} 2*e^(-2*Pi*k - 2*Pi).

%F Equals 1 + lim_{n->oo} (2*e^(-2*Pi*n))*(e^(2*Pi*n) - 1)/(e^(2*Pi) - 1). (End)

%e 1.003741873197321288201552691194800017462452422...

%p Tau := 2*Pi: Digits := 120: (exp(Tau) + 1)/(exp(Tau) - 1):

%p evalf(%)*10^110: ListTools:-Reverse(convert(floor(%), base, 10)); # _Peter Luschny_, May 21 2021

%t RealDigits[Coth[Pi], 10, 110][[1]] (* _Georg Fischer_, Apr 03 2020 *)

%Y Cf. A175314, A175315, A019692.

%K cons,nonn

%O 1,4

%A _R. J. Mathar_, Apr 01 2010

%E a(42) ff. corrected by _Georg Fischer_, Apr 03 2020