A294514 Decimal expansion of (3/2)*log(3) - Pi/(2*sqrt(3)).

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

Offset: 0

Author

Wolfdieter Lang, Nov 02 2017

Keywords

• nonn
• cons

Comments

This is the limit of the series V(3,2) := Sum_{k>=0} 1/((k + 1)*(3*k + 1)) = Sum_{k>=0} 1/A049450(k+1) = (1/2)*Sum_{k>=0} (3/(3*k + 1) - 1/(k+1)) with partial sums given in A250328(n+1)/A294513(n).

Examples

			0.7410187508850556117958287265627106908292027126877538898170990327...
		

References

• Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, pp. 189 - 193, with v_2(3) = (1/3)*V(3,2).

Crossrefs

Cf. A049450, A250328/A294513.

Programs

Mathematica

RealDigits[N[(3/2)*Log[3] - Pi/(2*Sqrt[3]), 157]][[1]] (* Georg Fischer, Apr 04 2020 *)

PARI

(3/2)*log(3) - Pi/(2*sqrt(3)) \\ Michel Marcus, Nov 02 2017

Formula

Equals V(3,2) = Sum_{k>=0} 1/((k + 1)*(3*k + 1)).

Equals Sum_{k>=2} zeta(k)/3^(k-1). - Amiram Eldar, May 31 2021

Extensions

a(100) ff. corrected by Georg Fischer, Apr 04 2020

Data truncated by Sean A. Irvine, Apr 10 2020