# Is there a difference between $g(x,y)$ and $g(x;y)$?

Is there a reason that the second notation uses a semicolon?

Here's the definition:

we say $$g(x;y)$$ is a Green's function

$$g(x;y) = \left\{ \begin{array}{lr} \sin(kx)\sin(k(y-1)/k\sin(k) & : x \lt y\\ \sin(ky)\sin(k(x-1)/k\sin(k) & : y \lt x\\ \end{array} \right.$$

• There is no difference, but the notation $g(x;y)$ suggests that we are going to think of $y$ as a parameter. For a fixed value of $y$, we will be interested in the function $x \mapsto g(x; y)$. It would have been ok to use the notation $g(x,y)$ instead, and some authors do this when discussing Green's functions. – littleO Jan 4 at 14:03
• @littleO it seems like you could make that comment verbatim into an answer – Mark S. Jan 4 at 14:15

There is no difference, but the notation $$g(x;y)$$ suggests that we are going to think of $$y$$ as a parameter. For a fixed value of $$y$$, we will be interested in the function $$x \mapsto g(x;y)$$. It would have been ok to use the notation $$g(x,y)$$ instead, and some authors do this when discussing Green's functions.