= Quartic truncation of the Bessel function J0
{title2=$J_0(\rho)\approx(1-\rho^2/8)^2$}
The regular power series has $J_0(\rho)=1-\rho^2/4+\rho^4/64-\cdots$. Its quartic truncation has a double zero at $\rho=\sqrt8$, giving a rough disc-well energy estimate $4\hbar^2/(\mu a^2)$. A truncation zero is not an exact Bessel zero or a rigorous eigenvalue bound. The double-root behavior particularly warns against treating a low-order local expansion as accurate far from its center.
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