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Manuscript Title: Prolate radial spheroidal wave functions.
Authors: T.A. Beu, R.I. Campeanu
Program title: PRSWFN
Catalogue identifier: ACEY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 30(1983)177
Programming language: Fortran.
Computer: FELIX C-256.
Operating system: SIRIS 2/3.
RAM: 10K words
Word size: 32
Keywords: General purpose, Two-centre frame, Radial spheroidal Wave functions, Expansion, Bessel functions.
Classification: 4.7.

Nature of problem:
The prolate radial spheroidal wave functions appear in a wide range of physical applications, and in particular in two-centre systems. The package PRSWFN contains six subprograms which compute these functions of both the first and second kind for any argument and accuracy.

Solution method:
The prolate radial spheroidal wave functions Rml(1,2)(c,Xi) are calculated by summing spherical Bessel series, the coefficients being calculated separately, once for all the values of Xi; first the ratios of two consecutive coefficients are calculated recursively and then the final values of the coefficients are obtained through a normalization procedure.

Restrictions:
The package can be in principle applied to calculate any Rml(1,2)(c,Xi). However, for high accuracy calculations of Rml(2)(c,Xi) with Xi close to unity and large m, the number of terms to be retained in the spherical Bessel series becomes very large, imposing large storage space and considerable computing time.

Running time:
For Xi=1.077, c=0.1, ERRB=10**-4 the number of terms in the Rml(2)(c,Xi) series is 52. The run of this case took 7.7 s, from which about 90% of the time was dedicated to the calculation of the coefficients. The test run took about 9 min.