erfc                 package:NORMT3                 R Documentation

_C_o_m_p_l_e_m_e_n_t_a_r_y _e_r_r_o_r _f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the complementary error function of a (possibly) complex
     valued argument. This function is $2/\sqrt{pi} \int_{z}^{\infty}
     \exp^{-t^2} dt$.

_U_s_a_g_e:

     erfc(z)

_A_r_g_u_m_e_n_t_s:

       z: Argument of complementary error function

_D_e_t_a_i_l_s:

     Computes the complementary error function of a (possibly) complex
     valued argument. This function is $2/\sqrt{pi} \int_{z}^{\infty}
     \exp^{-t^2} dt$. This function actually calls FORTRAN code
     (algorithm TOMS 680) which computes the Faddeeva's function and
     then with a slight modification obtains the erfc function of a
     complex-valued argument.

_V_a_l_u_e:

     The complementary error function of z

_A_u_t_h_o_r(_s):

     Guy P. Nason, Department of Mathematics, University of Bristol

_R_e_f_e_r_e_n_c_e_s:

     Poppe, G.P.M. and Wijers, C.M.J. (1990) More efficient computation
     of the complex error function. _ACM Transactions on Mathematical
     Software_, *16*, 38-46.

_S_e_e _A_l_s_o:

     'erf'

_E_x_a_m_p_l_e_s:

     erfc(0)
     #
     # Should give 1
     #
     erfc(1)
     #
     # Should give 0.1572992+0i
     #
     erfc(complex(re=1, im=1))
     #
     # Should give -0.3161513-0.1904535i
     #

