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\documentclass{article}
\usepackage{prodint}
\def\d{\mathrm{d}}
\begin{document}
This is \verb+\prodi+ in action: $\prod_i\prodi\alpha_i(\d u)$. How does it look?
\bigskip
Now two equations to test \verb+\Prodi+
\[
\prod_{i=1}^n\Prodi_0^\tau \left(1-\d A_i(u)\right)
\]
\[
\int_0^\infty \prod_{i=1}^n\Prodi_0^t\left(1-\lambda_i(u,z)\,\d u\right)\;\d F(z)\]
\bigskip
and one with \verb+\PRODI+
\[ \PRODI_0^t \left\{\int_0^u g(z)\,\d F(z)\right\}^2 \d u
\]
\end{document}
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