cp's OEIS Frontend

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

%I A377753 #29 Feb 12 2025 21:41:12
%S A377753 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,
%T A377753 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,
%U A377753 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
%N A377753 Decimal expansion of 8*G/Pi^2, where G is the Catalan's constant (A006752).
%D A377753 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.
%F A377753 Equals (Sum_{n>=1} (-1)^(n+1)/(2*n - 1)^2) / (Sum_{n>=1} 1/(2*n - 1)^2) (see Finch).
%F A377753 Equals 1/A242822. - _Hugo Pfoertner_, Nov 07 2024
%F A377753 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
%e A377753 0.7424537454215443259079279607988799424377218365...
%t A377753 RealDigits[8Catalan/Pi^2,10,100][[1]]
%o A377753 (PARI) 8*Catalan/Pi^2 \\ _Charles R Greathouse IV_, Nov 27 2024
%Y A377753 Cf. A002388, A006752, A218387, A242822 (see the second formula).
%K A377753 nonn,cons
%O A377753 0,1
%A A377753 _Stefano Spezia_, Nov 07 2024