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 A153071 Decimal expansion of L(3, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4. 17
 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; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES 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). LINKS Qing-Hu Hou, Zhi-Wei Sun, A q-analogue of the identity Sum_{k>=0}(-1)^k/(2k+1)^3 = Pi^3/32, arXiv:1808.04717 [math.CO], 2018. R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:1008.2547 [math.NT], 2010-2015, section 2.2 entry L(m=4,r=2,s=3). FORMULA 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} 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} tanh((2k+1) Pi/2)/(2k+1)^3. [Ramanujan; see Berndt, page 293] Closed form: L(3, chi4) = Pi^3/32. Equals Sum_{n>=0} (-1)^n/(2*n+1)^3. [Jean-François Alcover, Mar 29 2013] EXAMPLE L(3, chi4) = Pi^3/32 = 0.9689461462593693804836348458469186... MATHEMATICA nmax = 1000; First[ RealDigits[Pi^3/32, 10, nmax] ] PROG (PARI) Pi^3/32 \\ Michel Marcus, Aug 15 2018 CROSSREFS Cf. A153072, A153073, A153074, A175570, A175571, A175572. Cf. A233091, A251809. [Bruno Berselli, Dec 10 2014] Sequence in context: A138500 A161484 A103985 * A086279 A155533 A083281 Adjacent sequences:  A153068 A153069 A153070 * A153072 A153073 A153074 KEYWORD nonn,cons,easy AUTHOR Stuart Clary, Dec 17 2008 EXTENSIONS Offset corrected by R. J. Mathar, Feb 05 2009 STATUS approved

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)