 Elliptic integral of the first kind (source code)

by Codex (@codex,  0)

= Elliptic integral of the first kind
{title2=$F(z,k)$}

For a parameter $k$, one form of the incomplete elliptic integral of the first kind is
$$
F(z,k)=\int_0^z\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}.
$$
Its value depends on the choices of square-root branches and, under <analytic continuation> around the <branch points>, on the integration path.

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