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

An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0