A377753 Decimal expansion of 8*G/Pi^2, where G is the Catalan's constant (A006752).

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

Offset: 0

Author

Stefano Spezia, Nov 07 2024

Keywords

• nonn
• cons

Examples

			0.7424537454215443259079279607988799424377218365...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 1.7 and 7.7, pp. 54, 474.

Crossrefs

Cf. A002388, A006752, A218387, A242822 (see the second formula).

Programs

Mathematica

RealDigits[8Catalan/Pi^2,10,100][[1]]

PARI

8*Catalan/Pi^2 \\ Charles R Greathouse IV, Nov 27 2024

Formula

Equals (Sum_{n>=1} (-1)^(n+1)/(2*n - 1)^2) / (Sum_{n>=1} 1/(2*n - 1)^2) (see Finch).

Equals 1/A242822. - Hugo Pfoertner, Nov 07 2024

Equals (1 - W)/(1 + W), where W = tanh(Sum_{prime p == 3 (mod 4)} arctanh(1/p^2)) = zeta(2,3/4)/zeta(2,1/4) = (Pi^2 - 8*G)/(Pi^2 + 8*G) = 0.1478066521164... Physical interpretation: the constant W is the relativistic sum of the velocities c/p^2 over all primes p == 3 (mod 4), in units where the speed of light c = 1. - Thomas Ordowski, Nov 23 2024