Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Nov 19 2024 00:54:02
%S 3,1,5,1,2,1,2,0,0,2,1,5,3,8,9,7,5,3,8,2,1,7,6,8,9,9,4,2,2,4,8,6,8,8,
%T 5,5,6,6,4,5,5,1,9,3,5,4,5,1,4,8,5,2,4,3,8,4,7,0,5,4,0,3,5,7,3,8,4,2,
%U 5,9,8,3,7,6,8,2,7,4,6,1,2,1,6,1,0,8,6,9,4,3
%N Decimal expansion of L^4/15, 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 Pi^6/(60*Gamma(3/4)^8) = A092732/(60*A068465^8).
%F Equals Sum_{z is a Gaussian integer != 0} 1/z^4.
%F Equals G_4(i), where G_4 is the Eisenstein series of weight 4.
%e 3.15121200215389753821768994224868855664551935451...
%t First[RealDigits[Pi^6/(60*Gamma[3/4]^8), 10, 100]]
%Y Cf. A062539, A068465, A092732.
%Y Cf. A377999, A378128, A378129, A378130, A378131.
%K nonn,cons,easy
%O 1,1
%A _Paolo Xausa_, Nov 18 2024