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Search: id:A114984
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| A114984 |
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Coefficients of cubic equations in the form w^2=4*x^3-g2*x-g3 Wierstrass elliptic form whose solutions approximate zeta zeros. |
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+0
1
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| 200, 199, 442, 441, 684, 683, 926, 925, 1168, 1167, 1410, 1409, 1652, 1651, 1894, 1893, 2136, 2135, 2378, 2377, 2620, 2619, 2862, 2861, 3104, 3103, 3346, 3345, 3588, 3587, 3830, 3829, 4072, 4071, 4314, 4313, 4556, 4555, 4798, 4797, 5040, 5039, 5282
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Other good approximation functions are: 1/2+I*b[n]->1/2-I/LogIntegral[1/(2.85*n)] 1/2+I*b[n]->1/2-I/LogIntegral[1/(4.05*Sqrt[n])] These types of functions gives the root finding function in Mathematica a place to start in iterations.
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FORMULA
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f[n = 200 + 242*(n - 1); g2/4=(1-f[n]);g3/4=f[n]; (a(n),a)(n+1) = {g3/4,g2/4}
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EXAMPLE
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f[n_] = 200 + 242*(n - 1);
b = Table[Table[x /. NSolve[x^3 - (1 - f[n])*x + f[n] == 0, x][[m]], {m, 1, 3}], {n, 1, 25}]
gives roots like:
{-1., 0.5 - 14.1333*I, 0.5+ 14.1333*I},
{-1., 0.5 - 21.0178*I, 0.5 + 21.0178*I}
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MATHEMATICA
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f[n_] = 200 + 242*(n - 1); a = Flatten[Table[Abs[Coefficient[x^3 - (1 - f[n])*x + f[n], x, m]], {n, 1, 50}, {m, 0, 1}]]
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CROSSREFS
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Sequence in context: A033523 A094220 A035881 this_sequence A118118 A124472 A078492
Adjacent sequences: A114981 A114982 A114983 this_sequence A114985 A114986 A114987
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 22 2006
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