|
Search: id:A129406
|
|
|
| A129406 |
|
Expansion of L(3, chi3) in base 3, where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3. |
|
+0
16
|
|
| 2, 1, 2, 2, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 0, 2, 2, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 0, 2, 1, 1
(list; cons; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
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... = (0.2122121100201111101022022020002102211...)_3
|
|
MATHEMATICA
|
nmax = 1000; First[ RealDigits[4 Pi^3/(81 Sqrt[3]) - (1/2) * 3^(-nmax), 3, nmax] ]
|
|
CROSSREFS
|
Cf. A129404, A129405, A129407, A129408, A129409, A129410, A129411.
Cf. A129658, A129659, A129660, A129661, A129662, A129663, A129664, A129665
Sequence in context: A109649 A098199 A022828 this_sequence A123018 A100429 A049710
Adjacent sequences: A129403 A129404 A129405 this_sequence A129407 A129408 A129409
|
|
KEYWORD
|
nonn,cons,easy
|
|
AUTHOR
|
Stuart Clary (clary(AT)uakron.edu), Apr 15, 2007
|
|
EXTENSIONS
|
Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
|
|
|
Search completed in 0.002 seconds
|
