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

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

When x is numeric, sinint(x) is equivalent to Si(x).

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

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

$\mathrm{sinint}\left(M\right)$

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