[Math] Conventions for function notation with multiple variables

notation

Consider the following expression:

$x\cdot a\cdot b$

In programming you could define a function $f(x,a,b)$ to assign values to all the variables. However, since I cannot remember seeing such notation being used in purely mathematical context, I am somewhat unsure whether I can do this in my math paper.

Hence, I have two questions:

  1. Is it ok to define a function as $f(x,a,b)=x\cdot a\cdot b$?
  2. If yes, can I refer to this function later in the paper as simply $f(x)$, omitting the other two variables? I guess what I am asking is whether $f(x,a,b)=f(x)$?

Best Answer

Given your comments, my suggestion is to use indices: something like

For given values $a$ and $b$, we define the function $f_{ab}$ by $f_{ab}(x)=abx$; for example, $f_{2,\sqrt{3}}(x) = 2\sqrt{3}x$. When $a$ and $b$ are fixed and understood from context, we will often omit them and simply write $f(x)$ instead of $f_{ab}(x)$.

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