A084258 Decimal expansion of Sum_{k>=1} coth(Pi*k)/k^3.

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

Offset

1,2

Comments

Splitting the infinite sum Simon Plouffe unearthed a rapidly converging series for zeta(3).

References

Bruce C. Berndt, Ramanujan Notebook part II, Infinite series, Springer Verlag, p. 293.

Links

Table of n, a(n) for n=1..108.

Simon Plouffe, Formulae for zeta(2n+1).

Formula

Equals 7*Pi^3/180.

Example

1.20579964867832634015741225260949870230876122200664...

Mathematica

RealDigits[7*Pi^3/180, 10, 100][[1]] (* Amiram Eldar, May 31 2021 *)

Prog

(PARI) 7*Pi^3/180

Crossrefs

Cf. A000796.

Sequence in context: A140571 A078049 A021490 * A171016 A321205 A111352

Adjacent sequences: A084255 A084256 A084257 * A084259 A084260 A084261

Keyword

cons,nonn

Author

Benoit Cloitre, Jun 21 2003

Status

approved