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A276712
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Decimal expansion of zeta(3)/8.
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2
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1, 5, 0, 2, 5, 7, 1, 1, 2, 8, 9, 4, 9, 4, 9, 2, 8, 5, 6, 7, 4, 9, 6, 7, 2, 7, 0, 1, 8, 8, 9, 3, 1, 2, 4, 8, 8, 4, 5, 6, 2, 3, 2, 8, 6, 5, 4, 2, 5, 6, 2, 3, 6, 0, 2, 2, 4, 0, 3, 3, 9, 4, 4, 4, 1, 7, 7, 2, 9, 7, 7, 5, 7, 2, 3, 2, 8, 9
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OFFSET
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0,2
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REFERENCES
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James Dodson, The Mathematical Repository Containing Analytical Solutions of Five Hundred Questions: Mostly Selected from Scarce and Valuable Authors, (1748), page 375.
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LINKS
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Nick Lord, Problen 89.D, Problem Corner, The Mathematical Gazette, Vol. 89, No. 514 (2005), pp. 115-119; Solution, ibid., Vol. 89, No. 516 (2005), pp. 539-542.
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FORMULA
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Equals Sum_{n>=1} 1/(2n)^3 = 1/8 + 1/64 + 1/216 + 1/512 + ...
zeta(3)/8 + A233091 = Sum_{n>=1} 1/(2n+1)^3 + Sum_{n>=1} 1/(2n)^3 = zeta(3).
Equals Sum_{k>=1} (-1)^(k+1) * H(k)/(k+1)^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - Amiram Eldar, Jul 22 2020
Equals Integral_{x=0..Pi/4} log(sin(x))*log(cos(x))/(sin(x)*cos(x)) dx (Lord, 2005). - Amiram Eldar, Jun 23 2023
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EXAMPLE
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0.150257112894949285674967270188...
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MATHEMATICA
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RealDigits[(Zeta[3])/8, 10, 100][[1]]
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PROG
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(Sage) (zeta(3)/8).n(100)
(Magma) SetDefaultRealField(RealField(120)); L:=RiemannZeta(); Evaluate(L, 3)/8; // G. C. Greubel, Nov 24 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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