Appendix V

Appendix V
Complementary Error Function (erfc)

\text{erf} (\beta) = \frac{2}{\sqrt{\mu}}\int_{0}^{\beta}e^{-e^2}d \epsilon

\text{erf} (-\beta) = \text{-erf}\beta

\text{erfc} (-\beta) = 1 - \text{erf} (\beta)

\pmb{\beta} erf (\pmb{\beta}) erfc (\pmb{\beta})
0 0 1.0
0.05 0.056372 0.943628
0.1 0.112463 0.887537
0.15 0.167996 0.832004
0.2 0.222703 0.777297
0.25 0.276326 0.723674
0.3 0.328627 0.671373
0.35 0.379382 0.620618
0.4 0.428392 0.571608
0.45 0.475482 0.524518
0.5 0.520500 0.479500
0.55 0.563323 0.436677
0.6 0.603856 0.396144
0.65 0.642029 0.357971
0.7 0.677801 0.322199
0.75 0.711156 0.288844
0.8 0.742101 0.257899
0.85 0.770668 0.229332
0.9 0.796908 0.203092
0.95 0.820891 0.179109
1.0 0.842701 0.157299
1.1 0.880205 0.119795
1.2 0.910314 0.089686
1.3 0.934008 0.065992
1.4 0.952285 0.047715
1.5 0.966105 0.033895
1.6 0.976348 0.023652
1.7 0.983790 0.016210
1.8 0.989091 0.010909
1.9 0.992790 0.007210
2 0.995322 0.004678
2.1 0.997021 0.002979
2.2 0.998137 0.001863
2.3 0.998857 0.001143
2.4 0.999311 0.000689
2.5 0.999593 0.000407
2.6 0.999764 0.000236
2.7 0.999866 0.000134
2.8 0.999925 0.000075
2.9 0.999959 0.000041
3 0.999978 0.000022