Applications of the complex exponential integral

where z = x + iy. R and / denote the real and imaginary components respectively. The integral converges if the upper limit is <x>e", and is independent of a, so long as -if á a á è» |2]. To make Ei(z) a single-valued function a branch cut is made just below the negative real axis, including the origin, such that z = x + iy = pe' , — ir < 6 ¿ t. This means that when the integral is evaluated for a point on the negative real axis the contour must be indented above the pole at the origin. The values of Ei(z) are given in the tables for the region 0 < 9 g t; those for the region — *■ < 6 < 0 can be obtained from the relations Ei(z) = Ei(z), z = x — iy. Here, as usual, f(z) means the complex conjugate of f(z).