两个奇怪的含参二元函数

青青子衿

\begin{align*}
f_0(u,v)&=\frac{\sqrt{\left(1+pu\right)\left(1+u\right)\left(1-u\right)\left(1-qu\right)\,\,\,}-\sqrt{\left(1+pv\right)\left(1+v\right)\left(1-v\right)\left(1-qv\right)\,\,\,}}{u-v}\\
g_0(u,v)&=\frac{2+p+q+(p-q)(u+v)-(p+q+2pq)uv}{\sqrt{\left(1+pu\right)\left(1+u\right)\left(1-v\right)\left(1-qv\right)\,\,\,}+\sqrt{\left(1+pv\right)\left(1+v\right)\left(1-u\right)\left(1-qu\right)\,\,\,}}\\
f(u,v)&=f_0(u,v)^{2}+\left(p-q\right)\left(u+v\right)-pq\left(u+v\right)^{2}\\
g(u,v)&=g_0(u,v)^{2}-\left(p+1\right)\left(q+1\right)
\end{align*}