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Search: id:A088537
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| A088537 |
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Decimal expansion of Madelung's constant M2. |
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+0
2
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| 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; cons; graph; listen)
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OFFSET
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1,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 76-81
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, p 1568-1575.
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FORMULA
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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).
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EXAMPLE
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M2=-1.6155426267....
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MAPLE
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M2:=evalf(4*(sqrt(2)-1)*Zeta(1/2)*sum('(-1)^n/sqrt(2*n+1)', 'n'=0..infinity), 120); [From Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009]
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PROGRAM
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(PARI) DirBet=sumalt(n=0, (-1)^n/sqrt(2*n+1)); print(4.0*(sqrt(2)-1)*zeta(0.5)*DirBet) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 20 2007
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CROSSREFS
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Sequence in context: A010137 A011096 A021623 this_sequence A019847 A021946 A011439
Adjacent sequences: A088534 A088535 A088536 this_sequence A088538 A088539 A088540
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KEYWORD
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nonn,cons
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 16 2003
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 20 2007
Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 10 2009
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