# Perfecting the product integral (integral sign with loop at the top)

I want to use this symbol for the product integral: Perhaps with a bigger loop, too. What's the best way of building this notation?

I got it to work for just the integral sign itself.

\usepackage{adjustbox}

\def\Prodint
{\adjustbox{trim = 0pt 0pt 0pt 0.15\height, clip} {$\displaystyle\int$}
{\hspace{-0.45em} \mathrel{\raisebox{0.9em}{$\rho$}}}}

$$|\psi(t)\rangle=\Prodint U_t(dt)|\psi(0)\rangle$$ But its behaviour with (especially lower) limits is really bad.

$$|\psi(t)\rangle=\Prodint_0^T U_t(dt)|\psi(0)\rangle\ne\int_0^T U_t(dt)|\psi(0)\rangle$$ How can I get the lower limit to be placed like in the standard \int (see above for reference)?

If you're happy with the symbol, set the lower limit together with the integral, then add the upper limit to the whole block.

\documentclass{article}
\usepackage{amsmath}

\NewDocumentCommand{\Prodint}{e{^_}}{%
\mathop{}\!%
{%
\adjustbox{trim = 0pt -0.5pt 0pt 0.15\height, clip}{$\displaystyle\int\IfValueT{#2}{_{#2}}$}%
\hspace{-0.45em}%
\raisebox{0.9em}{$\rho$}%
}%
\IfValueT{#1}{^#1}%
\!\mathop{}%
}

\begin{document}

$\int_0^T f(t)\,dt \ne \Prodint_0^T f(t)\,dt$

\end{document} • Thanks. Question: did the addition of the -0.5pt to the trim actually change anything? It didn't change anything for me. Also, how do the e notation work -- do the ^ and _ just represent #1 and #2 but with fancier notation than using square brackets? Is there some documentation for this, where it can be used? – Abhimanyu Pallavi Sudhir Aug 19 at 8:47
• @AbhimanyuPallaviSudhir Without it the lower limit could be cut because characters may overshoot a bit. Try with 0pt and you'll see. – egreg Aug 19 at 9:41
• @egreg Thank you very very much to have help the user Abhimanyu Pallavi Sudhir. Always thank you and I write it with all my heart. – Sebastiano Aug 19 at 12:21