I can't tell anything about the math there. I can only sense
that the topic is related to
big O
notation and related, the little o notation. This is not my
field of expertise, so i am lost.
The original problem was a misleading character for the lower
case calligraphic letters, which do not exist.
Package physices provides the command
order
. We
already know that by now. My first thought was using something not looking
the same lilke a standard o (small letter oh). Package
stix provides a script and a fraktur alphabet. But
stix is not your only choice. There are many others. Please have
a look at the
LaTeX Font Catalogue (especially the
fonts with math support).
This has nothing to do with using xelatex or lualatex, it was
just a suggestion. LuaLaTeX will (in a while) supersede pdflatex,
that was my view of the future.
Having copied and modified (quite unaware of its contents) the
definition of
order
from package physics, all
remaining is the question of »What font do you want to use«.
Having a look at the wikipedia entry above, they just used the
normal math alphabet.
You can run the following with pdflatex, just as usual. Try
clicking on »open in writelatex« just above the code. I made some
comments, they might be helpful for you (or not) or help you to
understand my train of thought.
Code: Select all
\documentclass{article}
%Stix provides some math alphabets, also script and
%fraktur (gothic) ones
%\usepackage{stix}
%It is stated in the documentation of STIX that it should be
%loaded before amsmath
\usepackage{amsfonts,amsmath,amssymb,amsthm}
\usepackage{mathtools}%pathces some amsmath quircks
\newtheorem{thm}{Theorem}
\usepackage{physics}
%the following taken, but modified, from physics.sty
\ProvideDocumentCommand\littleordersymbol{}{o}
%\RenewDocumentCommand\littleordersymbol{}{{\mathsf o}}
%you set evreything there
\DeclareDocumentCommand\littleorder{ l m
}{\fbraces#1{\lparen}{\rparen}{\littleordersymbol}{#2}}
%this switches alphabets to palatino
\DeclareFontFamily{OT1}{pzc}{}
\DeclareFontShape{OT1}{pzc}{m}{it}{<-> s * [1.10] pzcmi7t}{}
\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it}
\newcommand{\indieNum}[3]{\mathpzc{i}_#1 \left( #2; #3 \right)}
%now using the regular i
\newcommand{\indieNumB}[3]{i_#1 \left( #2; #3 \right)}
\newcommand{\kay}{K_{r,r}}
\newcommand{\littleoh}[1]{\ensuremath{\mathop{}\mathopen{}\mathpzc{o}\mathopen{}\left(#1\right)}}
\begin{document}
\begin{gather*}
% \indieNum{t}{G; \mu} \\
%you did this (^) once, please check
%Your definition, using palatino i
\indieNum{t}{G}{\mu} \\
%using regular i
\indieNumB{t}{G}{\mu} \\
\end{gather*}
%please be aware, that using $$ math $$ is not recommendend
%with LaTeX. It's the old TeX syntax
%\[
% \mathscr{o} \quad
% \mathfrak{o}
%\] %commented out, provided by stix
\begin{thm}
$\forall c \in \left( -\infty, 1 \right)$ and $G \in \mathcal{G}_{\mathbb{N},r,r}$
\begin{equation*}
\indieNum{t}{G; \mu} =
\begin{cases}
\left( 1 + \order{\mu^{-\left(1+c\right)}} \right) \indieNum{t}{\kay}{\mu} &
$G$ \text{ contains a triangle} \\
%you were already in math mode for the G there,
%please see the next line
\left( 1 + \order{\mu^{-\left(2+c\right)}} \right) \indieNum{t}{\kay}{\mu} & G \text{ is triangle free}.
\end{cases}
\label{eq:Result}
\end{equation*}
Furthermore $\indieNum{t}{G}{\mu} \leq \indieNum{t}{\kay}{\mu}$ for infinitely many $\mu \in \mathbb{R}^+$.
\end{thm}
\begin{gather*}
o(x)\\
\littleorder{x}\\
% ^ both o letters are the same
\littleoh{x} \\
%this was using the palatino o
\end{gather*}
\end{document}
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.