A294518 Decimal expansion of 3*log(2) - Pi/2.

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

Offset: 0

Author

Wolfdieter Lang, Nov 07 2017

Keywords

• nonn
• cons

Comments

This is the value of the series V(4,3) = lim_{n->oo} V(4,3;n) with the partial sums V(4,3;n) = Sum_{k=0..n} 1/((k + 1)*(4*k + 3)) = Sum_{k=0..n} 1/A033991(k+1) = Sum_{k=0..n} (4/(4*k + 3) - 1/(k+1)) = A294516(n)/A294517(n).

In the Koecher reference v_4(3) = (1/4)*V(4,3) = (3/4)*log(2) + Pi/8 = 0.1271613037212348272550...

Examples

			0.5086452148849393090203746727347782621279157033...
		

References

• Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, pp. 189-193.

Crossrefs

Cf. A033991, A294516/A294517.

Programs

Mathematica

RealDigits[3*Log[2] - Pi/2, 10, 100][[1]] (* Amiram Eldar, May 31 2021 *)

Formula

V(4,3) = 3*log(2) - Pi/2.

Equals Sum_{k>=2} zeta(k)/4^(k-1). - Amiram Eldar, May 31 2021