What is the significance of the semicolon in the notation for parameter \alpha?

[gnome]

Given this statement "T^k_{s,i} is exponentially distributed, and the parameter \alpha in the distribution of T^k_{s,i} depends only on the maximum expected surplus S^k_{s,i} of seller i on the length T of the trading period, and on t_k, the time elapsed in the trading period. We write this dependence as

<br /> \mbox{\Huge \alpha = f_{s,i}(S^k_{s,i};\, t_k,\, T)}<br />
..."

In that last expression what is the significance of the separation of the S^k_{s,i} from the t_k, T by a semicolon, as contrasted with the separation of the latter two terms by a comma? It's clearly not accidental -- they follow this notation several times in the paper.

 

[derek e]

To the left of the semicolon are the variables, to the right are the parameters.
<br /> f(x) = m\cdot x + b<br /> or <br /> f(x;m,b) = m\cdot x + b<br />

 

[gnome]

Thanks, that's good to know. But then, what I quoted above seems to be an abuse of that notation. T is clearly a parameter, but wouldn't you consider t_k (elapsed time) a variable?

 

[derek e]

That sounds like a question for your function, which seems to be saying that it's a parameter.