1 ## Copyright (C) 2006 Sylvain Pelissier <sylvain.pelissier@gmail.com>
3 ## This program is free software; you can redistribute it and/or modify
4 ## it under the terms of the GNU General Public License as published by
5 ## the Free Software Foundation; either version 3 of the License, or
6 ## (at your option) any later version.
8 ## This program is distributed in the hope that it will be useful,
9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 ## GNU General Public License for more details.
13 ## You should have received a copy of the GNU General Public License
14 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
17 ## @deftypefn {Function File} {@var{y} =} Ci (@var{z})
18 ## Compute the cosine integral function defined by:
22 ## Ci(x) = | cos(t)/t dt
26 ## @seealso{cosint, Si, sinint, expint, expint_Ei}
35 y(real(z) == 0 & imag(z) >0) = 0.5*(expint_Ei(i.*y(real(z) == 0 & imag(z) >0))+expint_Ei(-i.*y(real(z) == 0 & imag(z) >0)))+ i.*pi./2;
36 y(real(z) == 0 & imag(z) <0) = 0.5*(expint_Ei(i.*y(real(z) == 0 & imag(z) <0))+expint_Ei(-i.*y(real(z) == 0 & imag(z) <0)))-i*pi./2;
37 y(real(z)>=0) = -0.5.*(expint_E1(i.*y(real(z)>=0) )+expint_E1(-i.*y(real(z)>=0) ));
38 y(real(z)<0) = -0.5.*(expint_E1(-i.*y(real(z)<0))+expint_E1(i.*y(real(z)<0)))+i*pi;