A331239 Decimal expansion of Sum_{k>=0} (-1)^k/AGM(1, 1+k).

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

Offset: 0

Author

Daniel Hoyt, Jan 13 2020

Keywords

• nonn
• cons

Comments

AGM(x, y) is the arithmetic-geometric mean of Gauss and Legendre.

This series is closely related to A188859 (Sum_{k>=0} (-1)^k/((1+(1+k))/2)) and A113024 (Sum_{k>=0} (-1)^k/sqrt(1+k)). The denominators of these alternating series differ by being arithmetic, geometric, or arithmetic-geometric means of 1 and k.

Examples

			0.6092151504524492287304733713491660511183939228565999735...
		

Crossrefs

Cf. A016627, A188859, A113024.

Programs

PARI

sumalt(k=0, (-1)^k/agm(1,1+k))