A377363 Decimal expansion of 12/Pi^2.

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

Offset: 1

Author

Stefano Spezia, Oct 26 2024

Keywords

• nonn
• cons

Examples

			1.215854203708053257326553558516731666852305296...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.4.4, p. 23.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 263.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000583, A000796, A002388, A005408, A013661, A059956.

Programs

Mathematica

RealDigits[12/Pi^2,10,100][[1]]

Formula

Equals 2/zeta(2) = 2*A059956.

12/Pi^2 = 1 + K_{n>=1} n^4/(2*n+1), where K is the Gauss notation for an infinite continued fraction. In the expanded form, 12/Pi^2 = 1 + 1^4/(3 + 2^4/(5 + 3^4/(7 + 4^4/(9 + 5^4/(11 + ...))))) (see Finch at p. 23).

Equals 1/A072691. - R. J. Mathar, Jul 21 2025