How to use "Noto Math" letter alone?

Question

There is the upright greek letter like \uppi in "Noto Math".

I want use it, but not through newtxmath package

I can't find the vf file about "Noto Sans Math RM", just find "Noto Sans Math MI" (italic math).

How to find "RM" and use it directly? In other word, at MWE after, font NotoSans-TLF should be replaced by Noto Sans Math RM, this question will be done. Thank you!

\documentclass[12pt]{beamer}
\usefonttheme{professionalfonts}
\usepackage[T1]{fontenc}
% \usepackage[notosans]{newtxmath} % not through it
\DeclareSymbolFont{letters}{OML}{notosansmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{notosansmi}{b}{it}
\DeclareMathAlphabet{\mathbold}{OML}{notosansmi}{b}{it}
\DeclareSymbolFont{operators}{OT1}{NotoSans-TLF}{m}{n}
\SetSymbolFont{operators}{bold}{OT1}{NotoSans-TLF}{bx}{n}
\DeclareMathAlphabet{\mathbf}{OT1}{NotoSans-TLF}{bx}{n}
\DeclareMathAlphabet{\mathit}{OT1}{NotoSans-TLF}{m}{it}
\SetMathAlphabet\mathit{bold}{OT1}{NotoSans-TLF}{bx}{it}
\begin{document}
\frame{
\Huge
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\mathrm e}\Big)^n\sqrt{2\uppi n}} =1 ]
vs
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\mathrm e}\Big)^n\sqrt{2\pi n}} =1 ]
}
\end{document}

Answer 1

Easier in Unicode, with the range= option of unicode-math package (compile with xelatex\lualatex).

MWE

\documentclass[12pt]{beamer}
\usepackage{xcolor}
\usefonttheme{professionalfonts}
\usepackage{unicode-math}
\setmainfont{Noto Serif}
\setmathfont{TexGyrePagellaMath}[Colour=blue]
\setmathfont{Noto Sans Math}[range={"03C0,"1D70B},Colour=red]
\begin{document}
\frame{
\Huge
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\symup{e}}\Big)^n\sqrt{2\uppi n}} =1 ]
vs
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\mathrm e}\Big)^n\sqrt{2\pi n}} =1 ]
}
\end{document}

\uppi certainly works and produces an upright pi, but Noto Sans Math font is not a math font in terms of Open Type font features.

One solution is to load a placeholder font (here, arbitrarily, TeX Gyre Pagella Math) and load a range from Noto Sans Math.

Or: load everything from Noto Sans Math:

MWE

\documentclass[12pt]{beamer}
\usepackage{xcolor}
\usefonttheme{professionalfonts}
\usepackage{unicode-math}
\setmainfont{Noto Serif}
\setsansfont{Noto Sans}
\setmathfont{TeXGyrePagellaMath}[Colour=blue]
\setmathfont{Noto Sans Math}[range={it/{num,latin}->sfup,
it/{greek}->up,
up/{greek},
up/{num,latin}->sfup,
},
Colour=red]
\begin{document}
\frame{
\Huge
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\symup{e}}\Big)^n\sqrt{2\uppi n}} =1 ]
vs
[ \lim_{n\to\infty}\frac{n!}{\Big(\dfrac{n}{\mathrm e}\Big)^n\sqrt{2\pi n}} =1 ]
}
\end{document}

Or any combination of ranges/fonts as desired.