A157293 Decimal expansion of zeta(3)/zeta(9).

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Comments

The product Product_{p = primes = A000040} (1+1/p^3+1/p^6). The product over (1+2/p^3+1/p^6) equals A157289^2.

Examples

			1.19964753964713... = (1+1/2^3+1/2^6)*(1+1/3^3+1/3^6)*(1+1/5^3+1/5^6)*(1+1/7^3+1/7^6)*...
		

Links

• R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011, eq. (23).

Crossrefs

Cf. A002117, A013667, A030078, A030516, A157289.

Programs

Maple

evalf(Zeta(3)/Zeta(9)) ;

Mathematica

RealDigits[Zeta[3]/Zeta[9], 10, 120][[1]] (* Amiram Eldar, May 26 2023 *)

Formula

Equals A002117/A013667 = Product_{i>=1} (1+1/A030078(i)+1/A030516(i)) .