I have the a summation of the following form:
$\sum_{M_1} \left[ { f(M_1-m_1,-M_1+m_1+\mu_1^\prime,\mu_1^\prime) \cdot \atop { \displaystyle g(M_1,-M_1+m_1+\mu_1^\prime,m_1+\mu_1^\prime) \cdot\atop \displaystyle h(M_1,-m_1,M_1-m_1) } }\right]$ Where $f$,$g$, and $h$ are functions of their arguments. I would like to instead express it as a triple summation of some new variables, but I'm not sure if the way I've done it is correct. Can I use:
\begin{array}(\alpha=M_1-m_1 \\ \beta=-M_1+m_1+\mu_1^\prime \\ \gamma=\mu_1^\prime \\ \delta=M_1 \\ \epsilon=m_1+\mu_1' \\ \phi=-m_1 \end{array}
to rewrite the sum instead as:
\sum_{\alpha}\sum_{\beta}\sum_{\delta} f(\alpha,\beta,\gamma)g(\delta,\beta,\epsilon)h(\delta,\phi,\alpha)$$?