A175316 Decimal expansion of coth(Pi).

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, 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, 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

Offset

1,4

Links

Table of n, a(n) for n=1..109.

Formula

Equals A175314 divided by A175315.

Equals (exp(tau) + 1)/(exp(tau) - 1), where tau = 2*Pi = A019692. - Peter Luschny, May 22 2021

From Wolfe Padawer, Jan 28 2023: (Start)

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

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

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

Example

1.003741873197321288201552691194800017462452422...

Maple

Tau := 2*Pi: Digits := 120: (exp(Tau) + 1)/(exp(Tau) - 1):
evalf(%)*10^110: ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, May 21 2021

Mathematica

RealDigits[Coth[Pi], 10, 110][[1]] (* Georg Fischer, Apr 03 2020 *)

Crossrefs

Cf. A175314, A175315, A019692.

Sequence in context: A272004 A010471 A077226 * A197145 A344427 A163335

Adjacent sequences: A175313 A175314 A175315 * A175317 A175318 A175319

Keyword

cons,nonn

Author

R. J. Mathar, Apr 01 2010

Extensions

a(42) ff. corrected by Georg Fischer, Apr 03 2020

Status

approved