The mathematical notation for mentioning variables names explicitly in a function assignment

functionsnotation

I have a function with two parameters: $f(s,t)$.

I want to assign to the function $\alpha$ and $\beta$: $f(\alpha,\beta)=5$.

But I don't want the reader to confuse $s$ and $t$ (the function's variables) from the values $\alpha$ and $\beta$.
I want to mention explcitly which is assigned to $s$ and which is assigned to $t$.

So I would like to denote it, for example, like this: $f(s=\beta,t=\alpha)=5$, or like this $f(s:\beta,t:\alpha)=5$.

Is there a convention for such a notation?
What is the correct notation?

Best Answer

You can write the function $f(s,t)$ evaluated at point $(\alpha, \beta)$ as

$$f(s,t)|_{\alpha,\beta}=5$$

even your notation is also widely used i.e. $$f(s=\beta,t=\alpha)=5$$

I don't think your last notation is used much for this purpose.

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