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Manuscript Title: MAPLE programs for converting series expansions to rational functions using the Levin transformation. Automatic generation of Fortran functions for numerical applications.
Authors: J. Grotendorst
Program title: LEVIN
Catalogue identifier: ABLG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 55(1989)325
Programming language: Maple.
Computer: IBM 3090-200E.
Operating system: VM/HPO 4.2, VM/XA SP REL. 2.
RAM: 1000K words
Word size: 32
Keywords: Computer algebra, General purpose, Utility, Levin transformation, Convergence acceleration, Taylor expansion, Asymptotic expansion, Rational approximation, Maple, Symbolic computation, Fortran code generation.
Classification: 4.14, 5.

Nature of problem:
The efficient and reliable evaluation of infinite series expansions is of great importance in physics and chemistry.

Solution method:
Using the symbolic computation system MAPLE Taylor series expansions and asymptotic series expansions are converted to rational functions via the Levin transformation. Automatic generation of FORTRAN functions for the resulting rational expressions is supported.

Restrictions:
The available computer storage is the severest restriction.

Running time:
It depends on the problem and cannot be estimated in advance. Using the Maple time function the test examples given took 4.4 cpu s on IBM 3090- 200E with VM/HPO 4.2 and 46.8 s on IBM 4381-1 with VM/XA SP Rel.2.