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Manuscript Title: A numerical evaluator for the generalized hypergeometric series.
Authors: W.F. Perger, A. Bhalla, M. Nardin
Program title: PFQ
Catalogue identifier: ACPA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 77(1993)249
Programming language: Fortran.
Computer: Sun SPARC Station.
Operating system: Sun OS 4.1.1, Sun OS 4.1.2, CMS VM/SP HOP 5.0, AIX 3.1.5.
RAM: 1600K words
Word size: 8
Keywords: General purpose, Special functions, Confluent hypergeometric, Function.
Classification: 4.7.

Nature of problem:
The generalized hypergeometric series is the solution of many equations occuring in various scientific and engineering disciplines. A couple of examples are: the radial part of the wavefunction of the hydrogen atom, for bound and continuum states both non-relativistic and relativistic, and the radial and angular parts of the solution to the biconical antenna.

Solution method:
The generalized hypergeometric series is summed using extended precision complex arrays.

The program is fundamentally limited by the amount of available memory. A PARAMETER statement sets the variable LENGTH, which is the maximum size of any of the extended precision arrays (the distributed version of PFQ has LENGTH=777).

Unusual features:
The program automatically estimates the number of bits available in the mantissa and sets the number of array positions required accordingly. The program also scans the input data looking for input parameters that would result in a division by zero or a finite series. In either case, the program examines the in coming parameter(s), comparing them against zero, considering the number of bits available in the mantissa. If a number is close enough to zero to meet this criterion, the program prints a message to the user and either continues or aborts, depending on the anticipated impact. The user options include the ability to request a specific number of significant figures in the result, whether or not to return the result in natural logarithm form, and the ability to manually or automatically determine the number of array elements to be used in the extended arithmetic.

Running time:
The running time may vary widely, on a given machine, depending on the number of terms required in the summation to achieve convergence. On a Sun SPARCStation 1, the time required has been observed to be as small as 1 second and as large as 20 minutes.