Programs in Physics & Physical Chemistry
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|Manuscript Title: Symbolic integration of a product of two spherical bessel functions with an additional exponential and polynomial factor|
|Authors: B. Gebremariam, T. Duguet, S. K. Bogner|
|Program title: SymbBesselJInteg|
|Catalogue identifier: AEFY_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 181(2010)1136|
|Programming language: Mathematica 7.1.|
|Computer: Any computer running Mathematica 6.0 and later versions.|
|Operating system: Windows Xp, Linux/Unix.|
|RAM: 256 Mb|
|Keywords: Symbolic integration, Spherical Bessel function.|
|PACS: 02.30.GP, 02.60.Jh.|
Nature of problem:
Nature of problem: Integration, both analytical and numerical, of products of two spherical bessel functions with an exponential and polynomial multiplying factor can be a very complex task depending on the orders of the spherical bessel functions. The Mathematica package discussed in this paper solves this problem using a novel symbolic approach.
The problem is first cast into a related limit problem which can be broken into two related subproblems involving exponential and exponential integral functions. Solving the cores of each subproblem symbolically sets the stage for an involved expression tree parsing and manipulation to obtain the most simplified analytic expression for the initial problem.
1 min for typical values of the arguments and can be several mins for large values of the input variables. For the test data included, about an hour.
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