These integrals are defined for all complex x as follows:

The functions Si, Ssi, and Shi are entire.  The functions Ci and Chi have a logarithmic singularity at the origin and have a branch cut along the negative real axis.

$\mathrm{Ci}\left(1.\right)$

$0.3374039229$

$\mathrm{Ci}\left(3\right)$

$\mathrm{Ci}\left(3\right)$

$\mathrm{evalf}\left(\right)$

$0.1196297860$

$\mathrm{Si}\left(3.14159+7.6\mathrm{I}\right)$

$63.60695388-123.1816272\mathrm{I}$

$\mathrm{Ssi}\left(12345.67890\right)$

$\mathrm{-0.00005756635677}$

$\mathrm{Si}\left(12345.67890\right)$

$1.570738760$

$\mathrm{Shi}\left(\mathrm{\pi }\right)$

$\mathrm{Shi}\left(\mathrm{\pi }\right)$

$\mathrm{Chi}\left(1.+\mathrm{I}\right)$

$0.8821721806+1.283547193\mathrm{I}$

$\mathrm{convert}\left(\mathrm{Ci}\left(x\right)\,\mathrm{Ei}\right)$

$-\frac{{\mathrm{Ei}}_1\left(\mathrm{I}x\right)}{2}-\frac{{\mathrm{Ei}}_1\left(\mathrm{-I}x\right)}{2}+\frac{\mathrm{I}\left(\mathrm{csgn}\left(x\right)-1\right)\mathrm{csgn}\left(\mathrm{I}x\right)\mathrm{\pi }}{2}$

Abramowitz, M. and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.