The cosine integral is defined for all complex x as follows:

When x is a container object such as an Array or list, the cosint(x) function computes the element-wise cosine integral of x.  For example when x is a Matrix the result R is formed as R[i,j] = Ci(x[i,j]).

When x is numeric, cosint(x) is equivalent to Ci(x).

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$x≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=-3+\mathrm{I}\right)\:$

$\mathrm{cosint}\left(x\right)$

$\left[\begin{array}{ccc}\mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }& \mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }& \mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }\\ \mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }& \mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }& \mathrm{Ci}\left(3-\mathrm{I}\right)+\mathrm{I}\mathrm{\pi }\end{array}\right]$