Always assuming $x>0$ and $z>0$, how about:
$$\begin{align}
x^y &={} \stackrel{y}{_x\triangle_{\phantom{z}}}&&\text{$x$ to the $y$}\\
\sqrt[y]{z} &={} \stackrel{y}{_\phantom{x}\triangle_{z}}&&\text{$y$th root of $z$}\\
\log_x(z)&={} \stackrel{}{_x\triangle_{z}}&&\text{log base $x$ of $z$}\\
\end{align}$$
The equation $x^y=z$ is sort of like the complete triangle $\stackrel{y}{_x\triangle_{z}}$. If one vertex of the triangle is left blank, the net value of the expression is the value needed to fill in that blank. This has the niceness of displaying the trinary relationship between the three values. Also, the left-to-right flow agrees with the English way of verbalizing these expressions. It does seem to make inverse identities awkward:
$\log_x(x^y)=y$ becomes $\stackrel{}{_x\triangle_{\stackrel{y}{_x\triangle_{\phantom{z}}}}}=y$. (Or you could just say $\stackrel{}{_x\stackrel{y}{\triangle}_{\stackrel{y}{_x\triangle_{\phantom{z}}}}}$.)
$x^{\log_x(z)}=z$ becomes $\stackrel{\stackrel{}{_x\triangle_{z}}}{_x\triangle_{\phantom{z}}}=z$. (Or you could just say $\stackrel{\stackrel{}{_x\triangle_{z}}}{_x\triangle_{z}}$.)
$\sqrt[y]{x^y}=x$ becomes $\stackrel{y}{\triangle}_{\stackrel{y}{_x\triangle_{\phantom{z}}}}=x$. (Or you could just say $\stackrel{}{_x\stackrel{y}{\triangle}_{\stackrel{y}{_x\triangle_{\phantom{z}}}}}$ again.)
$(\sqrt[y]{z})^y=z$ becomes $_{\stackrel{y}{_\phantom{x}\triangle_{z}}}\hspace{-.25pc}\stackrel{y}{\triangle}=z$. (Or you could just say $_{\stackrel{y}{_\phantom{x}\triangle_{z}}}\hspace{-.25pc}\stackrel{y}{\triangle}_z$.)
Having $3$ variables, I was sure that there must be $3!$ identities, but at first I could only come up with these four. Then I noticed the similarities in structure that these four have: in each case, the larger $\triangle$ uses one vertex (say vertex A) for a simple variable. A second vertex (say vertex B) has a smaller $\triangle$ with the same simple variable in its vertex A. The smaller $\triangle$ leaves vertex B empty and makes use of vertex C.
With this construct, two configurations remain that provide two more identities:
$_{\stackrel{y}{_\phantom{x}\triangle_{z}}}\hspace{-.25pc}\stackrel{}{\triangle_z}=y$ states that $\log_{\sqrt[y]{z}}(z)=y$.
$\stackrel{\stackrel{}{_x\triangle_{z}}}{_\phantom{x}\triangle_{z}}=x$ states that $\sqrt[\log_x(z)]{z}=x$.
I was questioning the usefulness of this notation until it actually helped me write those last two identities. Here are some other identities:
$$\begin{align}
\stackrel{a}{_x\triangle_{\phantom{z}}}\cdot\stackrel{b}{_x\triangle_{\phantom{z}}}&={}\stackrel{a+b}{_x\triangle_{\phantom{z}}}&
\frac{\stackrel{a}{_x\triangle_{\phantom{z}}}}{\stackrel{b}{_x\triangle_{\phantom{z}}}}&={}\stackrel{a-b}{_x\triangle_{\phantom{z}}}&
_{\stackrel{a}{_x\triangle_{\phantom{z}}}}\hspace{-.25pc}\stackrel{b}{\triangle}
&={}\stackrel{ab}{_x\triangle_{\phantom{z}}}\\
\stackrel{}{_x\triangle_{ab}}&={}\stackrel{}{_x\triangle_{a}}+\stackrel{}{_x\triangle_{b}}&
\stackrel{}{_x\triangle_{a/b}}&={}\stackrel{}{_x\triangle_{a}}-\stackrel{}{_x\triangle_{b}}&\stackrel{}{_x\triangle}_{\stackrel{b}{_a\triangle_{\phantom{z}}}}&=b\cdot\stackrel{}{_x\triangle}_{a}
\\
\stackrel{-a}{_x\triangle_{\phantom{z}}}&=\frac{1}{\stackrel{a}{_x\triangle_{\phantom{z}}}}&
\stackrel{1/y}{_x\triangle_{\phantom{z}}}&=\stackrel{y}{_\phantom{x}\triangle_{x}}&
\stackrel{}{_x\triangle_{1/a}}&=-\mathord{\stackrel{}{_x\triangle_{a}}}\\
\stackrel{}{_a\triangle_{b}}\cdot\stackrel{}{_b\triangle_{c}}&=\stackrel{}{_a\triangle_{c}}&
\stackrel{}{_a\triangle_{c}}&=\frac{\stackrel{}{_b\triangle_{c}}}{\stackrel{}{_b\triangle_{a}}}&
\stackrel{\stackrel{-n}{_y\triangle_{\phantom{z}}}}{_x\triangle_{\phantom{z}}}&=\stackrel{\stackrel{n}{_y\triangle_{\phantom{z}}}}{_\phantom{x}\triangle_{x}}&
\end{align}$$
There are no standard rules. Writers of maths are allowed to use whatever letters they like for things, and different writers are allowed to use different letters. Most people follow some unwritten conventions, but different users of maths use different conventions. Users in the same discipline area who write to each other a lot tend to use the same conventions, but even then there are differences.
There are some common conventions (but by no means set in stone):
- Areas and volumes often use capital letters, while lengths often use small letters
- Bold letters are usually used to mean vectors, though some writers do not use bold for vectors, and others mark them in a different way
- In linear algebra, a matrix is usually a capital letter
- In calculus, small letters are usually used for functions, with a capital letter often reserved for a function which is the integral of some other function
- In geometry, capital letters are usually used for points, small english letters for lines and small greek letters for planes (including $\pi$)
- $\pi$ is usually reserved for the number $\pi$ in places where that number is likely to appear. In other places, it is used to mean a probability or a profit or a projection or a permutation.
- small e is not a common choice for a letter in a scientific formula, because it can be used to mean the number $e$. However in ordinary algebra it can be used for a coefficient, especially if you have already used a, b, c, d
None of those are hard-and-fast rules, but simply observations of how people tend to write.
Note that there are more concepts in the world than letters that can represent them, so a letter E is not always energy, but represents whatever the writer has chosen it to represent today. Hence you should always tell your reader what the letters stand for. Sometimes we are sloppy if we think the reader understands already. For example, when we write "$E = mc^2$" we should technically write "$E = mc^2$, where $E$ is energy, $m$ is mass, and $c$ is the speed of light in a vacuum", but we generally assume people know a bit about this particular formula already. Most of the time, though, you should be very clear what you mean by each letter the first time you use it.
Another point about good writing is that in one piece of writing, you shouldn't change your notation mid-way. This is very frustrating to the reader! (Imagine if an author changed the name of their main character partway through a novel!)
The final point, which is actually a proper rule is that captital/small/bold/curly letters are not interchangeable. If a capital $E$ is used for something in a piece of writing, then you can't use a small $e$ elsewhere to mean the same thing. In short, maths is "case sensitive".
Best Answer
The $Q$ is a parameter, and $q$ is a variable ranging from $0$ to $Q$: basically, you have $Q+1$ parameters $\textrm{ceps}_0,\dots, \textrm{ceps}_Q$; or, in programming terms, you have an array $\textrm{ceps}[0\dots Q]$.
Similarly, the LPC coefficients are a list of $p$ values $a_1,\dots, a_p$ (i.e., $a_q$ for $q=1\dots p$), where $p$ is another parameter.
The recursion procedure explains how to compute value $Q+1$ values in $\textrm{ceps}[0\dots Q]$, recursively, starting with $\textrm{ceps}[0]$ and then applying the formula: $$ \textrm{ceps}[1] = a_1 + \sum_{k=1}^0 \frac{k-1}{1}a_k \textrm{ceps}[1-k] = a_1 $$ then $$ \textrm{ceps}[2] = a_2 + \sum_{k=1}^1 \frac{k-2}{2}a_k \textrm{ceps}[2-k] = a_2 - \frac{1}{2}a_1 \textrm{ceps}[1] = a_2-\frac{a_1^2}{2} $$ etc.