A157295 Decimal expansion of 630/Pi^6.

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

Offset: 0

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Examples

			0.655301728176386946536... = (1-1/2^2+1/2^4-1/2^6)*(1-1/3^2+1/3^4-1/3^6)*(1-1/5^2+1/5^4-1/5^6)*(1-1/7^2+1/7^4-1/7^6)*...
		

Links

• Masato Kobayashi, Möbius functions of higher rank and Dirichlet series, arXiv:2108.01822 [math.NT], 2021.
• Index entries for transcendental numbers.

Crossrefs

Cf. A013661, A013662, A013666, A001248, A030514, A030516, A092746, A363551.

Programs

Maple

evalf(630/Pi^6) ;

Mathematica

RealDigits[630/Pi^6, 10, 120][[1]] (* Amiram Eldar, Jun 10 2023 *)

PARI

630/Pi^6 \\ Michel Marcus, Aug 05 2021

Formula

Equals Product_{p primes = A000040} (1-1/p^2+1/p^4-1/p^6).

Equals A013662/(A013661*A013666).

Equals Product_{i>=1} (1-1/A001248(i)+1/A030514(i)-1/A030516(i)).

Equals 630*A092746.

Equals Sum_{n>=1} A363551(n)/n^2. - Amiram Eldar, Jun 10 2023