Cauchy Integral Formula and Electrodynamics

Is it possible to solve for an E field from a charge density function using the Cauchy Integral Formulas from complex variables?

Cauchy Integral Formula about a closed loop in the complex plane
(Integral[f[z]/ (z-z0)^(n+1)dz = 2 pi i /n! d^n f(z0)/dz ])

that is the n derivative of f with respect to z evaluated at z0