##### Q = {3} ##### complement Q = [3] c_0 = prod(1-1/p) = 0.66666666666666666667 predicted ratio E_Q(1,2) = prod(1-2/p) = 0.33333333333333333333 k f_k^all - 1 f_k^P - c_0 ratio 24 -1.39024994617e-6 -4.03002246422e-7 0.28987754866076 28 -1.23822662255e-7 -3.68149849322e-8 0.29732025028258 32 -1.04913874857e-8 -3.17486334385e-9 0.30261615521949 36 -8.55842447549e-10 -2.623768189e-10 0.30657140184067 40 -6.77789793498e-11 -2.09875173708e-11 0.30964640618884 44 -5.24150770902e-12 -1.63584644035e-12 0.31209463596473 deviation from the prediction, scaled by k (should tend to a constant if the ratio approaches E_Q(1,2) with a 1/k correction): k=24 E_Q(1,2) - ratio = 0.043455785 k*(that) = 1.0429388 k=28 E_Q(1,2) - ratio = 0.036013083 k*(that) = 1.0083663 k=32 E_Q(1,2) - ratio = 0.030717178 k*(that) = 0.9829497 k=36 E_Q(1,2) - ratio = 0.026761931 k*(that) = 0.96342953 k=40 E_Q(1,2) - ratio = 0.023686927 k*(that) = 0.94747709 k=44 E_Q(1,2) - ratio = 0.021238697 k*(that) = 0.93450268 ratio at k=44 : 0.3120946359647292 one-term (L + a/k) extrapolation : 0.336576933723581 two-term (L + a/k + b/k^2) extrapol.: 0.3332266315289948 predicted E_Q(1,2) : 0.3333333333333333 relative error of the two-term fit : 0.00032010541 ##### Q = {5} ##### complement Q = [5] c_0 = prod(1-1/p) = 0.8 predicted ratio E_Q(1,2) = prod(1-2/p) = 0.6 k f_k^all - 1 f_k^P - c_0 ratio 24 -1.39024994617e-6 -7.57120724446e-7 0.54459324133137 28 -1.23822662255e-7 -6.8548968625e-8 0.55360599890814 32 -1.04913874857e-8 -5.87660819463e-9 0.56013641690653 36 -8.55842447549e-10 -4.83616159622e-10 0.56507615508756 40 -6.77789793498e-11 -3.85631875273e-11 0.56895497538086 44 -5.24150770902e-12 -2.99848628654e-12 0.5720656065004 deviation from the prediction, scaled by k (should tend to a constant if the ratio approaches E_Q(1,2) with a 1/k correction): k=24 E_Q(1,2) - ratio = 0.055406759 k*(that) = 1.3297622 k=28 E_Q(1,2) - ratio = 0.046394001 k*(that) = 1.299032 k=32 E_Q(1,2) - ratio = 0.039863583 k*(that) = 1.2756347 k=36 E_Q(1,2) - ratio = 0.034923845 k*(that) = 1.2572584 k=40 E_Q(1,2) - ratio = 0.031045025 k*(that) = 1.241801 k=44 E_Q(1,2) - ratio = 0.027934393 k*(that) = 1.2291133 ratio at k=44 : 0.5720656065004031 one-term (L + a/k) extrapolation : 0.6031719176958619 two-term (L + a/k + b/k^2) extrapol.: 0.6000559362346761 predicted E_Q(1,2) : 0.6 relative error of the two-term fit : 9.3227058e-5