Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

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Manuscript Title: f1: a code to compute Appell's F_{1} hypergeometric
function. | ||

Authors: F.D. Colavecchia | ||

Program title: f1 | ||

Catalogue identifier: ADSJ_v1_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 157(2004)32 | ||

Programming language: Fortran 90. | ||

Computer: PC, SGI Origin2*. | ||

Operating system: Linux, IRIX. | ||

RAM: 1K words | ||

Word size: 32 | ||

Keywords: Numerical methods, Special functions, Hypergeometric functions, Appell functions, Gauss function, General purpose, Function. | ||

Classification: 4.7. | ||

Nature of problem:Computing the Appell F_{1} function is relevant in atomic
collisons and elementary particle physics. It is usually the result of
multidimensional integrals involving Coulomb continuum states. | ||

Solution method:The F_{1} function has a convergent-series definition for
|x|< 1 and |y| < 1, and several analytic continuations for
other regions of the variable space. The code tests the values of the
variables and selects one of the precedent cases. In the convergence
region the program uses the series definition near the origin of
coordinates, and a numerical integration of the third-order
differential parametric equation for the F_{1} function
Also detects several special cases according to the values of the | ||

Restrictions:The code is restricted to real values of the variables { x,y}. Also, there are some parameter domains that are
not covered. These usually imply differences between integer parameters
that lead to negative integer arguments of Gamma functions. | ||

Running time:Depends basically on the variables. The computation of table 4 (64 functions) requires approximately 0.33 seconds in a Athlon 900 MHz processor. |

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