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 A088537 Decimal expansion of Madelung's constant M2. 11
 1, 6, 1, 5, 5, 4, 2, 6, 2, 6, 7, 1, 2, 8, 2, 4, 7, 2, 3, 8, 6, 7, 9, 2, 3, 3, 3, 2, 7, 5, 8, 6, 1, 8, 0, 9, 0, 1, 9, 6, 4, 2, 2, 9, 2, 3, 6, 1, 3, 7, 7, 7, 1, 4, 5, 6, 9, 3, 7, 3, 5, 3, 5, 9, 6, 1, 2, 6, 5, 1, 2, 3, 1, 6, 1, 5, 3, 3, 3, 6, 2, 9, 0, 4, 1, 6, 5, 8, 9, 5, 5, 1, 7, 1, 8, 7, 2, 1, 4, 5, 5, 7, 4, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 76-81. LINKS I. J. Zucker, Exact results for some lattice sums in 2, 4, 6 and 8 dimensions, J. Phys. A: Math., Gen. vol. 7 (1974) no. 13, pp. 1568-1575. FORMULA M2 = Sum_{ -oo < i < oo, -oo < j < oo, (i,j) != (0,0) } (-1)^(i + j)/sqrt(i^2 + j^2)). M2 = 4*(sqrt(2) - 1)*zeta(1/2)*beta(1/2) (beta=Dirichlet beta function). EXAMPLE M2 = -1.6155426267.... MAPLE M2:=evalf(4*(sqrt(2)-1)*Zeta(1/2)*sum('(-1)^n/sqrt(2*n+1)', 'n'=0..infinity), 120); # Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009 MATHEMATICA (2-2*I)*(Sqrt[2]-1)*Zeta[1/2]*(PolyLog[1/2, -I]-Zeta[1/2, 1/4]) // Re // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Feb 15 2013 *) PROG (PARI) DirBet=sumalt(n=0, (-1)^n/sqrt(2*n+1)); print(4.0*(sqrt(2)-1)*zeta(0.5)*DirBet) ; \\ R. J. Mathar, Jul 20 2007 CROSSREFS Cf. A059750. Sequence in context: A021623 A197296 A177838 * A325313 A019847 A021946 Adjacent sequences:  A088534 A088535 A088536 * A088538 A088539 A088540 KEYWORD nonn,cons AUTHOR Benoit Cloitre, Nov 16 2003 EXTENSIONS More terms from R. J. Mathar, Jul 20 2007 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009 STATUS approved

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Last modified May 14 19:38 EDT 2021. Contains 343902 sequences. (Running on oeis4.)