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Decimal expansion of 2*Pi^6/945.
1

%I #8 Oct 01 2022 14:19:45

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

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

%U 6,4,3,6,5,8,0,3,9,1,5,7,9,5,7,6,5,5,4,7,9,5,5,8,7,7,0,7,0,3,4,1,0,6

%N Decimal expansion of 2*Pi^6/945.

%D L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, (2008) p. 15.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series.</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F 2*Pi^6/945 = 2*zeta(6) = G_6(infinity), where the function G_k(z) is the Eisenstein nonzero modular form of weight k.

%e 2.034686123968898279429035859581841055803634980065707123684817328...

%t RealDigits[2*Pi^6/945, 10, 102] // First

%o (PARI) 2*Pi^6/945 \\ _Charles R Greathouse IV_, Oct 01 2022

%Y Cf. A013664, A092732, A257134.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Apr 16 2015