While studying the wikipedia article about elliptic integrals, I encountered this notation, which I do not understand.
$F(\varphi,k) = F(\varphi \,|\, k^2) = F(\sin \varphi ; k) = \int_0^\varphi \frac {d\theta}{\sqrt{1 - k^2 \sin^2 \theta}}$
What do those separators
- $F(\cdot,\cdot)$
- $F(\cdot|\cdot)$
- $F(\cdot;\cdot)$
of the arguments of $F$ mean explicitly?