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Decimal expansion of 3*sqrt(2)*Pi^3/128.
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%I #35 Dec 17 2023 03:05:41

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

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

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

%N Decimal expansion of 3*sqrt(2)*Pi^3/128.

%C Equals the value of the Dirichlet L-series of the non-principal character modulo 8 (A188510) at s=3. - _Jianing Song_, Nov 16 2019

%D L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 64 (formula 340).

%H G. C. Greubel, <a href="/A251809/b251809.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Equals Sum_{i >= 0} (-1)^floor(i/2)/(2i+1)^3 = +1 +1/3^3 -1/5^3 -1/7^3 +1/9^3 +1/11^3 - ...

%F Equals Sum_{i >= 1} A188510(i)/i^3 = Sum_{i >= 1} Kronecker(-8,i)/i^3. - _Jianing Song_, Nov 16 2019

%F Equals 1/(Product_{p prime == 1 or 3 (mod 8)} (1 - 1/p^3) * Product_{p prime == 5 or 7 (mod 8)} (1 + 1/p^3)). - _Amiram Eldar_, Dec 17 2023

%e 1.027722585936858567879256618002255767210100318536997465331084755185...

%t RealDigits[3 Sqrt[2] Pi^3/128, 10, 90][[1]]

%o (PARI) 3*sqrt(2)*Pi^3/128 \\ _G. C. Greubel_, Jul 27 2018

%o (Magma) R:= RealField(); 3*Sqrt(2)*Pi(R)^3/128; // _G. C. Greubel_, Jul 27 2018

%Y Cf. A153071: Sum_{i >= 0} (-1)^i/(2i+1)^3.

%Y Cf. A233091: Sum_{i >= 0} 1/(2i+1)^3.

%Y Cf. A093954, A188510.

%K nonn,cons

%O 1,3

%A _Bruno Berselli_, Dec 10 2014