|
| |
|
|
A129411
|
|
Greedy Egyptian expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
|
|
15
| |
|
|
2, 3, 20, 1449, 2879423, 31625640285294, 1162849840832612010600369938, 4013794377413687199924671384130798842309412001723286013, 32025095658857878502181254937184611855940944199483548417530154807379258429933254996925647878294253643673560013
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Contributed to OEIS on Apr 15, 2007 --- the 300th anniversary of the birth of Leonhard Euler.
|
|
|
REFERENCES
| Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 176 and 292
|
|
|
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))
|
|
|
EXAMPLE
| L(3, chi3) = 0.8840238117500798567430579168710118077... = 1/2 + 1/3 + 1/20 + 1/1449 + 1/2879423 + ...
|
|
|
MATHEMATICA
| nmax = 12; prec = 2000 (* Adjust the precision depending on nmax. *); c = N[ 4 Pi^3/(81 Sqrt[3]), prec]; First@Transpose@NestList[{Ceiling[1/(#[[2]] - 1/#[[1]])], #[[2]] - 1/#[[1]]}&, {Ceiling[1/c], c}, nmax - 1]
|
|
|
CROSSREFS
| Cf. A129404, A129405, A129406, A129407, A129408, A129409, A129410.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A110372 A132421 A132500 * A124447 A024765 A090122
Adjacent sequences: A129408 A129409 A129410 * A129412 A129413 A129414
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
|
| |
|
|
