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

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

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.
$$f(x) = m\cdot x + b$$ or $$f(x;m,b) = m\cdot x + b$$

 

[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.