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

Question

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 https://tex.stackexchange.com/q/480768 for instructions to "build your own". — , Aug 17 '19 at 10:12
Excuse me but where have you finded this symbol? I have not seen this symbol into your link. — Sebastiano, Aug 17 '19 at 15:25
You should check out https://ctan.org/tex-archive/info/symbols/comprehensive/?lang=en, but I doubt you will find it. — John Kormylo, Aug 17 '19 at 15:28
@Sebastiano I have not. I just thought it would be a cool symbol to use. — Abhimanyu Pallavi Sudhir, Aug 17 '19 at 16:42
@AbhimanyuPallaviSudhir Yes I have understood. But is there a link where have you taken the image? — Sebastiano, Aug 17 '19 at 18:58
@Sebastiano I made it in Paint. By attaching \rho to the integral sign. — Abhimanyu Pallavi Sudhir, Aug 18 '19 at 03:25
@AbhimanyuPallaviSudhir Ah ok. Infact your symbol not exist. You can see this question and best answer of the user Jhor https://tex.stackexchange.com/questions/428066/different-mathcalj. You should cut two symbols and glue them into exact position. — Sebastiano, Aug 18 '19 at 08:24
@Sebastiano Thanks! I managed to make the sign itself -- do you know how I can correct the positions of the limits (see the updated question)? — Abhimanyu Pallavi Sudhir, Aug 19 '19 at 07:05
@AbhimanyuPallaviSudhir I hope I helped you a little bit. You have to say thanks to the excellent user egreg not to me :-). — Sebastiano, Aug 19 '19 at 12:20

score 4 · Accepted Answer · answered Aug 19 '19 at 08:42

4

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}
\usepackage{adjustbox,xparse}

\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}

answered Aug 19 '19 at 08:42

egreg

1,121,712

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 '19 at 08:47
@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 '19 at 09:41
@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 '19 at 12:21

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

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