R-Integral symbol for my notes

Question

I am typing up a set of notes for the Riemann Stieltjes integral. For reasons beyond the scope of the question, I would like to start with defining the Darboux's integral and then formulate Riemann's definition and show that they are equivalent.

During the intermediate steps, provisionally, I would like to define the Riemann integral, the R-integral. To avoid mixing of symbols, I have in mind a symbol like \oint but with a R instead of the circle.

I am not aware of what the TeX code for the symbol would be.

Any help would be appreciated.

Answer 1

You may try with the following code:

\documentclass{article}
\usepackage{mathtools}
\newcommand{\Rint}{\mathop{\mathrlap{\pushR}}\!\int}
\newcommand{\pushR}{\mathchoice
  {\mkern2.5mu R}
  {\scriptstyle R}
  {\scriptscriptstyle R}
  {\scriptscriptstyle R}
}
\begin{document}
\[
\left|\Rint_a^b f\right|\textstyle\left|\Rint_a^b f\right|_{\left|\Rint_a^b f\right|}
\]
\end{document}

The absolute value is only for demonstration purpose.

The main problem here is to adapt the R to the various formula styles, so we use \mathchoice. With \mathrlap we can build a zero width box that will not contribute to the width of the formula. Since \int is an operator, we put this zero width formula into a \mathop, then \! is used to remove the space that TeX inserts between two consecutive Operator atoms.

Next we define \pushR, that's simply a space in display style, followed by a normal size R. In text and lower styles we simply put a reduced size R. Probably the result will not be nice in \scriptscriptstyle, but it doesn't seem so important.

The same idea can be used for the principal value integral:

\newcommand{\pvint}{\mathop{\mathrlap{\pushpv}}\!\int}
\newcommand{\pushpv}{\mathchoice
  {\mkern5mu\rule[.6ex]{.5em}{1pt}}
  {\mkern2.8mu\rule[.5ex]{.35em}{.8pt}}
  {\mkern2.5mu\rule[.29ex]{.3em}{.7pt}}
  {\mkern2mu\rule[.2ex]{.2em}{.5pt}}
}