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A129404
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Decimal expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
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16
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8, 8, 4, 0, 2, 3, 8, 1, 1, 7, 5, 0, 0, 7, 9, 8, 5, 6, 7, 4, 3, 0, 5, 7, 9, 1, 6, 8, 7, 1, 0, 1, 1, 8, 0, 7, 7, 4, 7, 9, 4, 6, 1, 8, 6, 1, 1, 7, 6, 5, 8, 9, 3, 4, 7, 8, 2, 5, 8, 7, 4, 1, 4, 7, 4, 9, 1, 1, 5, 6, 6, 7, 0, 3, 3, 3, 2, 3, 1, 8, 7, 0, 1, 6, 3, 5, 9, 6, 3, 6, 4, 6, 8, 9, 5, 5, 3, 6, 0, 6
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Contributed to OEIS on April 15, 2007 --- the 300th anniversary of the birth of Leonhard Euler.
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REFERENCES
| Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 176 and 292
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FORMULA
| 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
| L(3, chi3) = 0.8840238117500798567430579168710118077...
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MATHEMATICA
| nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 10^(-nmax), 10, nmax] ]
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CROSSREFS
| Cf. A129405, A129406, A129407, A129408, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A073447 A011213 A178728 * A117040 A085669 A154012
Adjacent sequences: A129401 A129402 A129403 * A129405 A129406 A129407
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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