A355922 Decimal expansion of Sum_{k>=2} (1/k)*arctanh(1/k).

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

Offset: 0

Author

Amiram Eldar, Jul 21 2022

Keywords

• nonn
• cons

Examples

			0.67656513614796664082647201...
		

Links

• Michael Ian Shamos, Shamos's Catalog of the Real Numbers, 2011, p. 564.

Crossrefs

Cf. A016655, A355921, A355923.

Programs

Mathematica

RealDigits[N[Sum[ArcTanh[1/k]/k, {k, 2, Infinity}], 30], 10, 26][[1]] (* Amiram Eldar, Jul 21 2022 *)

Formula

Equals Sum_{k>=2} arccoth(k)/k.

Equals Sum_{k>=1} (zeta(2*k)-1)/(2*k-1).

Equals log(Product_{k>=2} ((k+1)/(k-1))^(1/(2*k))).

Extensions

More terms from Jinyuan Wang, Jul 21 2022