I have to compute $\operatorname{erf}(z)$ using the Fresnel integrals. I have the relation:
$$C(z)+iS(z)=\frac{1+i}{2}\operatorname{erf}\left[ \frac{\sqrt{\pi}}{2}(1-i)z \right].$$
But $\operatorname{erf}(z)$ has a complex argument. I've tried to make it real, but I didn't get a correct relation.
Can anybody help me?
Thank you very much.