# Term for a 'coefficient' used in multiple places.

Consider the case where I have a 'coefficient' $T$ such that:

$f(x) = T(1 - e^{-x/T})$

What would you call this term? It's certainly being used as a 'coefficient', but its reciprocal is also being used in exponentiation. Most definitions I have found for coefficient specify multiplication, which is as I have used it as well.

Is there a canonical term for this type of term?

Edit: I should note that in my usage, this will be constant for most applications but it's technically changeable, as this is an optimizable 'constant'. I have considered simply using 'constant' since during the lifetime of the usage of the equation this shouldn't change, but it seems odd to denote a configurable/changeable value as a 'constant'.

• "Parameter" works in this context sometimes, particularly when you plan to study different $f$'s that you get by changing $T$. May 23, 2016 at 20:44
• I would use "arbitrary constant." That way, it's clear the constant doesn't refer to a fixed number. You could also say that it's a function of two variables, $f(x,T)$, or that it is a family of functions $f_T(x)$.
– Neil
May 23, 2016 at 20:45
• @LeeMosher Parameter definitely seems apt! Now I'm a little disappointed by myself as we are even using Parameter in similar but different contexts. May 23, 2016 at 20:46
• @Neil In this case I have to think of the user experience and so I don't know if using "arbitrary" provides that. Defining it as a function of two variables seems like it would work, though that also implies to me that the value will be changing more than it does. May 23, 2016 at 20:52