How can I express that a symbol $f_\alpha$ is contextually associated with a symbol $\alpha$ but without implying that $f_\alpha$ depends on $\alpha$?

Question

Lets say I have the two symbols $\alpha$, $\beta$ and another two symbols, which are contextually associated with $\alpha$, $\beta$. For example $a$, $b$ as factors for a formula $a \cdot \alpha + b \cdot \beta$.

From a notation point of view, how can I express that $a$ is a factor associated with $\alpha$ and $b$ is a factor associated with $\beta$?

One possibility would be to replace $a,b$ by something like $f_\alpha$, $f_\beta$. However, this has the disadvantage that one might think $f_\alpha$ depends on a specific value $\alpha$.

Answer 1

I would also use indices, but in a different way. For instance, it si quite common to write $$c_1X_1 + c_2X_2 + c_3X_3,$$ for instance for a system of equation. In such an expression, $c_i$ does not depend on $X_i$, but is nevertheless associated to $X_i$, thanks to the index $i$. You could perhaps use the same idea for your formula.

Answer 2

I think you stylistically have it right with $f_\alpha$. If the value depended on $\alpha$, I would expect to see it written as $f(\alpha)$.

As with everything else in math notation, you should be clear in your writing how you expect readers to interpret your symbols if you are concerned about misunderstandings.