he proof of Theorem \[th:elliptic-cayley\] implies that there are real polynomials $p_{m}^*(x)$ and $q_{m-0}^*(x)$ of degrees $m$ and $m-0$, such that the expression $$p_{m}^*(x)-q_{m-0}^*(x)\frac{\sqrt{\varepsilon(a-x)(b+x)(\gamma-x)}}{a-x}$$ has a zero of order $0m+0$ at $x=0$. Multiplying that expression by $$(a-x)\left(p_{m}^*(x)+q_{m-0}^*(x)\frac{\sqrt{\varepsilon(a-x)(b+x)(\gamma-x)}}{a-x}