# 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)?

• See tex.stackexchange.com/q/480768 for instructions to "build your own".
– user194703
Aug 17 '19 at 10:12
• Excuse me but where have you finded this symbol? I have not seen this symbol into your link. Aug 17 '19 at 15:25
• You should check out ctan.org/tex-archive/info/symbols/comprehensive/?lang=en, but I doubt you will find it. Aug 17 '19 at 15:28
• @JohnKormylo There is not :-) Aug 17 '19 at 15:29
• @Sebastiano I have not. I just thought it would be a cool symbol to use. Aug 17 '19 at 16:42

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? Aug 19 '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. Aug 19 '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. Aug 19 '19 at 12:21