linguistic:voice_change, structural:expansion
Exponential integral of imaginary argument

If z {\displaystyle z} is imaginary, it has a nonnegative real part, so we can use the formula

to get a relation with the trigonometric integrals Si {\displaystyle \operatorname {Si} } and Ci {\displaystyle \operatorname {Ci} }:

The real and imaginary parts of E 1 (i x) {\displaystyle \mathrm {E} _{1}(ix)} are plotted in the figure to the right with black and red curves.