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A251809
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Decimal expansion of 3*sqrt(2)*Pi^3/128.
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10
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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, 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, 5, 7, 7, 7, 2, 4, 6, 8, 5, 8, 4, 9, 6, 8, 0, 3, 5, 1
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OFFSET
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1,3
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COMMENTS
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Equals the value of the Dirichlet L-series of the non-principal character modulo 8 (A188510) at s=3. - Jianing Song, Nov 16 2019
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REFERENCES
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L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 64 (formula 340).
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LINKS
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FORMULA
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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 - ...
Equals Sum_{i >= 1} A188510(i)/i^3 = Sum_{i >= 1} Kronecker(-8,i)/i^3. - Jianing Song, Nov 16 2019
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
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EXAMPLE
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1.027722585936858567879256618002255767210100318536997465331084755185...
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MATHEMATICA
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RealDigits[3 Sqrt[2] Pi^3/128, 10, 90][[1]]
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PROG
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(Magma) R:= RealField(); 3*Sqrt(2)*Pi(R)^3/128; // G. C. Greubel, Jul 27 2018
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CROSSREFS
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Cf. A153071: Sum_{i >= 0} (-1)^i/(2i+1)^3.
Cf. A233091: Sum_{i >= 0} 1/(2i+1)^3.
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KEYWORD
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AUTHOR
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STATUS
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approved
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