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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

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

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user29418
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    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 04 '19 at 14:03
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    @littleO it seems like you could make that comment verbatim into an answer – Mark S. Jan 04 '19 at 14:15

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I'll post my comment here so that the question receives an answer:

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
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