Landen transformations and the integration of rational functions (Q2781214)
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scientific article; zbMATH DE number 1720965
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Landen transformations and the integration of rational functions |
scientific article; zbMATH DE number 1720965 |
Statements
19 March 2002
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Landen transformation
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elliptic integrals
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rational functions
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0.8910801
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0.87786096
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0.8686123
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0.86800754
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Landen transformations and the integration of rational functions (English)
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A rational version of the classical Landen transformation for elliptic integrals is presented. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm for numerical integration of these functions. The reduction formula is proved. The variety of closed-form evaluations of integrals of rational functions, in particular symmetric and nonsymmetric functions of different degrees is given. In the Appendix the closed-form evaluation of two sums involving binomial coefficients is produced with the purpose to simplify expressions.
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