Could anyone help me, how to analyse real and imaginary parts of erf function?

I have a problem, in the theory of diffraction of Gaussian beams, in a perfectly infnit plane. The result is geven in the form of erf function.

[the cyclist]

Your question has too little information for anyone to help you. You need to put more effort into your question, if you want people to be able to understand your problem.

Answer 1

[Walter Roberson]

If you were hoping that you would be able to decompose erf(x) in to independent real and imaginary parts that could (potentially) each be simplified... then the answer appears to be that there is no way to do that.

For example, real(erf(3+i*A)) has a modest positive peak near A=3.665, but goes steeply negative after A=3.668 -- and goes even more steeply positive somewhere near 4.1 .