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Decimal expansion of 56 * Pi^7 / (98415 * sqrt(3)).
3

%I #25 Aug 06 2024 05:50:18

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

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

%U 1,8,1,0,1,3,5,5,9,0,3,3,0,6,4,3,0,8,2

%N Decimal expansion of 56 * Pi^7 / (98415 * sqrt(3)).

%D L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (310).

%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).

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

%F Equals 2^3 * 7 * Pi^7 / (3^9 * 5 * sqrt(3)).

%F Equals 1 + Sum_{k>=1} ( 1/(3*k+1)^7 - 1/(3*k-1)^7 ).

%F Equals Product_{p prime} (1 - Kronecker(-3, p)/p^7)^(-1) = Product_{p prime != 3} (1 + (-1)^(p mod 3)/p^7)^(-1). - _Amiram Eldar_, Nov 06 2023

%e 0.9922365295225111693516317453513060...

%t RealDigits[56 * Pi^7 / (98415 * Sqrt[3]), 10, 120][[1]] (* _Amiram Eldar_, Jun 07 2023 *)

%Y Cf. A129404, A344778, A344688.

%K nonn,cons

%O 0,1

%A _Sean A. Irvine_, Aug 17 2021