Let $V\in C_c^\infty(\mathbb R^3;\mathbb R)$ be radial, write $V(x)=V(r)$ with $r=|x|$, and fix $k>0$ such that $E=\hbar^2k^2/(2m)$ is neither a threshold nor an embedded eigenvalue. For each $\ell\ge0$, let $u_\ell:(0,\infty)\to\mathbb R$ solve the radial equation \begin{align*} -\frac{\hbar^2}{2m}u_\ell''(r) +\left(V(r)+\frac{\hbar^2\ell(\ell+1)}{2mr^2}\right)u_\ell(r) =Eu_\ell(r), \end{align*} with the regular boundary condition $u_\ell(r)\sim r^{\ell+1}$ as $r\to0$ and the asymptotic normalization \begin{align*} u_\ell(r)\sim \sin\left(kr-\frac{\ell\pi}{2}+\delta_\ell(k)\right) \end{align*} as $r\to\infty$. If the scattering amplitude is normalized by \begin{align*} \psi_k^{(+)}(x)=e^{ik\cdot x}+f(\theta)\frac{e^{ikr}}{r}+o(r^{-1}), \end{align*} where $\theta$ is the angle between the incoming and outgoing directions, then the fixed-energy amplitude has the partial wave expansion \begin{align*} f(\theta) = \frac{1}{k}\sum_{\ell=0}^{\infty}(2\ell+1)e^{i\delta_\ell(k)}\sin(\delta_\ell(k))P_\ell(\cos\theta), \end{align*} where $P_\ell$ is the $\ell$th Legendre polynomial. The series converges to the amplitude in $L^2(S^2)$, and pointwise at angles where the Legendre series of the amplitude converges.