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A100220
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Decimal expansion of Product_{k>=1} (1 - 1/3^k).
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27
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5, 6, 0, 1, 2, 6, 0, 7, 7, 9, 2, 7, 9, 4, 8, 9, 4, 4, 9, 6, 9, 7, 9, 2, 2, 4, 3, 3, 1, 4, 1, 4, 0, 0, 1, 4, 3, 7, 9, 7, 3, 6, 3, 3, 3, 7, 9, 8, 3, 6, 2, 4, 6, 4, 4, 6, 2, 9, 5, 6, 2, 9, 7, 3, 1, 7, 5, 3, 3, 9, 6, 3, 0, 8, 9, 0, 3, 3, 7, 9, 4, 7, 0, 7, 7, 1, 6, 9, 1, 8, 7, 7, 0, 5, 3, 6, 7, 4, 3, 3, 4, 8
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OFFSET
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0,1
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COMMENTS
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Limit of the probability that a random N X N matrix, with entries chosen independently and uniformly from the field F_3, is nonsingular [Morrison (2006)]. - L. Edson Jeffery, Jan 22 2012
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LINKS
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FORMULA
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Product_{k >= 1} (1 - 1/3^k) = (1/3; 1/3)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 27 2015
Constant C = (1 - 1/3)*Sum_{n >= 0} (-1/3)^n/Product_{k = 1..n} (3^k - 1);
C = (1 - 1/3)*(1 - 1/9)*Sum_{n >= 0} (-1/9)^n/Product_{k = 1..n} (3^k - 1);
C = (1 - 1/3)*(1 - 1/9)*(1 - 1/27)*Sum_{n >= 0} (-1/27)^n/Product_{k = 1..n} (3^k - 1), and so on. (End)
Equals sqrt(2*Pi/log(3)) * exp(log(3)/24 - Pi^2/(6*log(3))) * Product_{k>=1} (1 - exp(-4*k*Pi^2/log(3))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027871(n). (End)
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EXAMPLE
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0.56012607792794894496979224331414001437973633379836...
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MATHEMATICA
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(3^(1/24)*EllipticThetaPrime[1, 0, 1/Sqrt[3]]^(1/3))/2^(1/3).
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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