Editing Exponential integral (section)

===Exponential integral of imaginary argument===

[[Image:E1ofImaginaryArgument.png|right|200px|thumb|<math>E_1(ix)</math>
against <math>x</math>; real part black, imaginary part red.]]

If <math>z</math> is imaginary, it has a nonnegative real part, so we can use the formula
:<math>
E_1(z) = \int_1^\infty
\frac{e^{-tz}} t \, dt
</math>
to get a relation with the [[trigonometric integral]]s <math>\operatorname{Si}</math> and <math>\operatorname{Ci}</math>:
:<math>
E_1(ix) = i\left[ -\tfrac{1}{2}\pi + \operatorname{Si}(x)\right] - \operatorname{Ci}(x)
\qquad (x > 0)
</math>
The real and imaginary parts of <math>\mathrm{E}_1(ix)</math> are plotted in the figure to the right with black and red curves.