A code to evaluate prolate and oblate spheroidal harmonics Original Research Article

We present a code to evaluate prolate (Pnm(x), Qnm(x); n ≥ m, x > 1) and oblate (Pnm(ix), Qnm(ix); n ≥ m, x > 0) spheroidal harmonics, that is, spherical harmonics (n and m integers) for real arguments larger than one and for purely imaginary arguments. We start from the known values (in closed form) of Pmm and Pm+1m and we apply the forward recurrence relation over n up to a given degree n = NMax. The Wronskian relating Pʹs and Qʹs, together with the evaluation of the continued fraction for Qm+NstaggeredMaxm/Qm+NstaggeredMax-1m, allows the calculation of Qm+NstaggeredMaxm and Qm+NstaggeredMax-1m. Backward recurrence is then applied to generate the Qʹs. We show an application of the algorithm.