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A103133
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Decimal expansion of Dirichlet series L_{-7}(2).
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5
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1, 1, 5, 1, 9, 2, 5, 4, 7, 0, 5, 4, 4, 4, 9, 1, 0, 4, 7, 1, 0, 1, 6, 9, 2, 3, 9, 7, 3, 2, 0, 5, 4, 9, 9, 6, 4, 7, 9, 7, 8, 2, 1, 4, 0, 4, 6, 8, 6, 5, 6, 6, 9, 1, 4, 0, 8, 3, 9, 6, 8, 6, 3, 6, 1, 6, 6, 1, 2, 4, 1, 6, 3, 4, 5, 4, 5, 9, 1, 5, 4, 7, 5, 5, 6, 6, 7, 7, 5, 1, 9, 0, 6, 2, 9, 7, 2, 1, 2, 5, 3, 4
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OFFSET
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1,3
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 98-99.
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FORMULA
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(Psi(1, 1/7) + Psi(1, 2/7) - Psi(1, 3/7) + Psi(1, 4/7) - Psi(1, 5/7) - Psi(1, 6/7))/49, where Psi(1, x) is the polygamma function of order 1.
Equals 1/(Product_{p prime == 1, 2 or 4 (mod 7)} (1 - 1/p^2) * Product_{p prime == 3, 5 or 6 (mod 7)} (1 + 1/p^2)). - Amiram Eldar, Dec 17 2023
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EXAMPLE
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1.151925470544491047...
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MATHEMATICA
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(PolyGamma[1, 1/7] + PolyGamma[1, 2/7] - PolyGamma[1, 3/7] + PolyGamma[1, 4/7] - PolyGamma[1, 5/7] - PolyGamma[1, 6/7])/49 // RealDigits[#, 10, 102]& // First
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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