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Search: id:A129408
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| A129408 |
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Continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. |
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+0
16
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| 0, 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, 1, 2, 27, 1, 28, 1, 2, 2, 3, 2, 7, 1, 1, 19, 1, 8, 3, 3, 2, 1, 10, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 35, 1, 2, 91, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 16, 1, 2, 2, 1, 2, 6, 1, 1, 6, 14, 1, 5, 5, 14, 2, 8, 1, 1, 1, 1, 2, 4, 2, 10, 37, 1, 10, 2, 4, 5, 4, 5, 24, 1, 2, 7, 1
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contributed to OEIS on April 15, 2007 --- the 300th anniversary of the birth of Leonhard Euler.
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REFERENCES
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Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 176 and 292
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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 A049347 shifted.
Series: L(3, chi3) = sum_{k=1..infinity} chi3(k) k^{-3} = 1 - 1/2^3 + 1/4^3 - 1/5^3 + 1/7^3 - 1/8^3 + 1/10^3 - 1/11^3 + ...
Closed form: L(3, chi3) = 4 pi^3/(81 sqrt(3))
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EXAMPLE
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L(3, chi3) = 0.8840238117500798567430579168710118077... = [0; 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 9, 4, 13, 4, ...]
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MATHEMATICA
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nmax = 1000; ContinuedFraction[4 Pi^3/(81 Sqrt[3]), nmax + 1]
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CROSSREFS
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Cf. A129404, A129405, A129406, A129407, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A117825 A010143 A101027 this_sequence A140213 A091258 A072101
Adjacent sequences: A129405 A129406 A129407 this_sequence A129409 A129410 A129411
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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), Apr 15, 2007
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