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Manuscript Title: A program for computing the conical functions of the first kind Pm(- 1/2+i*tau)(x) for m=0 and m=1.
Authors: K.S. Kolbig
Program title: FCONIC
Catalogue identifier: AAQH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)51
Programming language: Fortran.
Computer: CDC 7600.
Operating system: CDC SCOPE.
RAM: 2K words
Word size: 60
Keywords: General purpose, Conical Function, Legendre function, Spherical functions, Boundary value problems, Integral transforms, Mehler-fock transform, Asymptotic expansions.
Classification: 4.7.

Nature of problem:
The conical functions Pm(-1/2+i*tau)(x) appear in a wide range of physical applications. Here we mention boundary value problems for the Laplace equation in regions bounded by cones, by two intersecting spheres, or by one or two confocal hyperboloids of revolution. Further, these functions are used in the Mehler-Fock integral transform for problems in potential and heat theory, and in elementary particle physics.

Solution method:
Series expansions based on Gaussian hypergeometric functions evaluated by direct summation or rational approximations are used together with asymptotic expansions for real X > -1 and real tau >=0.

Running time:
A running time of about 300 mus on a CDC 7600 was found on the average. For x>0 and tau>20, the time reduces to about 200 mus on the average.