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Search: id:A153071
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| A153071 |
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Decimal expansion of L(3, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4 |
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+0
5
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| 9, 6, 8, 9, 4, 6, 1, 4, 6, 2, 5, 9, 3, 6, 9, 3, 8, 0, 4, 8, 3, 6, 3, 4, 8, 4, 5, 8, 4, 6, 9, 1, 8, 6, 0, 0, 0, 6, 9, 5, 4, 0, 2, 6, 7, 6, 8, 3, 9, 0, 9, 6, 1, 5, 4, 4, 2, 0, 1, 6, 8, 1, 5, 7, 4, 3, 9, 4, 9, 8, 4, 1, 1, 7, 0, 8, 0, 3, 3, 1, 3, 6, 7, 3, 9, 5, 9, 4, 0, 7
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Leonhard Euler, ``Introductio in Analysin Infinitorum'', First Part, Articles 175, 284 and 287
Bruce C. Berndt, ``Ramanujan's Notebooks, Part II'', Springer-Verlag, 1989. See page 293, Entry 25 (iii).
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FORMULA
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chi4(k) = Kronecker(-4, k); chi4(k) is 0, 1, 0, -1 when k reduced modulo 4 is 0, 1, 2, 3, respectively; chi4 is A101455.
Series: L(3, chi4) = sum_{k=1..infinity} chi4(k) k^{-3} = 1 - 1/3^3 + 1/5^3 - 1/7^3 + 1/9^3 - 1/11^3 + 1/13^3 - 1/15^3 + ...
Series: L(3, chi4) = sum_{k=0..infinity} tanh((2k+1) pi/2)/(2k+1)^3 [Ramanujan; see Berndt, page 293]
Closed form: L(3, chi4) = pi^3/32
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EXAMPLE
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L(3, chi4) = 0.9689461462593693804836348458469186...
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MATHEMATICA
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nmax = 1000; First[ RealDigits[Pi^3/32, 10, nmax] ]
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CROSSREFS
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Cf. A153072, A153073, A153074
Sequence in context: A138500 A161484 A103985 this_sequence A086279 A155533 A083281
Adjacent sequences: A153068 A153069 A153070 this_sequence A153072 A153073 A153074
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KEYWORD
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nonn,cons,easy
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AUTHOR
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Stuart Clary (clary(AT)uakron.edu), Dec 17, 2008
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EXTENSIONS
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Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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