I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using Mathematica. Here it is the code for the function.
U=(1/4+I/4) 1/k Sqrt[\[Pi]] /Sqrt[ k R] E^(-((I k (R^2+L^2))/(2 R))) (-erfi((1/2+I/2) 1 /Sqrt[k R] (R-Sqrt[d^2+L^2]))-erfi((1/2+I/2) 1 /Sqrt[ k R] (Sqrt[d^2+L^2]+R))+erfi((1/2+I/2) 1 /Sqrt[k R] (R-L))+erfi((1/2+I/2) 1 /Sqrt[ k R] (R+L)))
For example for simplicity taking some values constants, let's say k = 1; R = 1; d = 1;. It is possible to approximate using series, finally the real part is needed to have physical meaning and interpretation.