Using a semicolon in a functin argument. eg. f = f(x, y; t)

[mikeph]

Hi
I've seen this a few times, where we say f = f(x, y; t) for example, without a proper definition or any guidelines of usage. In my mind I read this as "f is a function over x and y, but it is also dependent on t although this is usually a fixed parameter", even though we might have some function like

f(x,y;t) = yx²/t

i.e. from looking at the form of f, you could not tell which variables would go either side of the semicolon.

Perhaps it can also be read as f being a family of functions over (x,y), where each is parametrised by t. But then this is just semantics, the maths is no different, so what's the point in the semicolon?

Does anyone know a better definition of this notation?

Thanks
Mike

 

[jedishrfu]

I think its your second definition of a set of surfaces in 3-space with varying 't' value.

 

[jbunniii]

Perhaps it can also be read as f being a family of functions over (x,y), where each is parametrised by t. But then this is just semantics, the maths is no different, so what's the point in the semicolon?

There is no mathematical need for the semicolon. The notations $f(x,y;t)$ and $f(x,y,t)$ mean the same thing. The semicolon is there because the author wants to group the function parameters in some way, hopefully for the convenience of the reader: perhaps $x$ and $y$ are spatial coordinates and $t$ is time.

 

[mikeph]

Ah, perfect. That is exactly what I want to do.

Thanks!