Let $\mu$ denote the Möbius function, and define the the Mertens function $M(x) = \sum_{n \leq x} \mu(n)$. By Person's formula, one can express $M(x)$ as a sum over the nontrivial zeros of the Riemann zeta function. However, in every book or paper I have come across, this is done assuming the simplicity of the zeta zeros.

My question: is there an expression for $M(x)$ involving a sum over the Riemann zeros, that can be obtained without assuming the simplicity of the zeros ?