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Search: id:A129410
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| A129410 |
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Pierce 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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| 1, 8, 13, 16, 64, 6951, 206515, 344040, 11364380, 14595803, 136951831, 417525297, 691111129, 982473113, 15154864245, 17661539909, 31435459113, 49634203300, 1454188399688, 2112564552862, 2266989878695, 5056833185437, 8740145960744
(list; graph; listen)
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OFFSET
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1,2
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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... = 1/1 - 1/(1*8) + 1/(1*8*13) - 1/(1*8*13*16) + 1/(1*8*13*16*64) - ...
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MATHEMATICA
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nmax = 100; prec = 3000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Floor[ 1/(1 - #[[1]] #[[2]]) ], 1 - #[[1]] #[[2]]}&, {Floor[1/c], c}, nmax - 1]
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CROSSREFS
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Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A080361 A054295 A057486 this_sequence A070112 A070113 A006613
Adjacent sequences: A129407 A129408 A129409 this_sequence A129411 A129412 A129413
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KEYWORD
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nonn,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
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