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What is the formula for the MGF about the mean?

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$\\begin{align*} \\text{For } \\mu &= E[X] \\\\ M_X(s) &= E[e^{s(X-\\mu)}] \\\\ M_X(s) &= E[e^{sX}e^{-\\mu s}] \\\\M_X(s) &= e^{-\\mu s} E[e^{sX}] \\\\ M_X(s) &= e^{-\\mu s} m_X(s) \\end{align*}$

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