A377999 - OEIS

%I #7 Nov 16 2024 07:25:40

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

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

%U 4,9,0,7,7,9,5,2,3,4,7,5,4,2,1,1,0,3,8,2,5,5

%N Decimal expansion of L^4/(80*Pi^4) - 1/240, where L is the lemniscate constant (A062539).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lemniscate_constant">Lemniscate constant</a> (includes this constant).

%H <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>.

%F Equals (3*Pi^2/Gamma(3/4)^8 - 4)/960 = (3*A002388/A068465^8 - 4)/960.

%F Equals Sum_{k >= 1} A001158(k)*exp(-2*Pi*k).

%e 0.001899012051119622176926758348328622030968310773034...

%t First[RealDigits[(3*Pi^2/Gamma[3/4]^8 - 4)/960, 10, 100]] (* or *)

%t First[RealDigits[Sum[DivisorSigma[3, k]*Exp[-2*Pi*k], {k, Infinity}], 10, 100]]

%Y Cf. A001158, A002388, A062539, A068465.

%K nonn,cons,easy

%O -2,2

%A _Paolo Xausa_, Nov 15 2024