  The standard algorithm for the numerical evaluation of the prolate spheroidal
wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;\gamma^2)$ of order $0$,
bandlimit $\gamma > 0$ and characteristic exponent $n$ has running time which
grows with both $n$ and $\gamma$. Here, we describe an alternate approach which
runs in time independent of these quantities. We present the results of
numerical experiments demonstrating the properties of our scheme, and we have
made our implementation of it publicly available.
