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Search: id:A153066
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| A153066 |
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Continued fraction for L(2, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. |
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+0
4
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| 0, 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 4, 1, 1, 1, 10, 1, 2, 1, 1, 1, 6, 1, 12, 2, 14, 1, 1, 1, 3, 3, 1, 1, 3, 1, 1, 12, 3, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 4, 2, 1, 12, 140, 1, 6, 3, 3, 1, 2, 1100, 4, 1, 1, 2, 1
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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chi3(k) = Kronecker(-3, k); chi3(k) is 0, 1, -1 when k reduced modulo 3 is 0, 1, 2, respectively; chi3 is A102283.
Series: L(2, chi3) = sum_{k=1..infinity} chi3(k) k^{-2} = 1 - 1/2^2 + 1/4^2 - 1/5^2 + 1/7^2 - 1/8^2 + 1/10^2 - 1/11^2 + ...
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EXAMPLE
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L(2, chi3) = 0.781302412896486296867187429624092... = [0; 1, 3, 1, 1, 2, 1, 17, 1, 10, 1, 1, 5, 1, 1, 2, 1, ...]
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MATHEMATICA
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nmax = 1000; ContinuedFraction[(Zeta[2, 1/3] - Zeta[2, 2/3])/9, nmax + 1]
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CROSSREFS
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Cf. A086724, A153067, A153068
Sequence in context: A080847 A095276 A089338 this_sequence A126209 A073166 A050169
Adjacent sequences: A153063 A153064 A153065 this_sequence A153067 A153068 A153069
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Dec 17, 2008
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