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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Landen transformations and the integration of rational functions


Authors: George Boros and Victor H. Moll
Journal: Math. Comp. 71 (2002), 649-668
MSC (2000): Primary 33-XX
Published electronically: November 9, 2001
MathSciNet review: 1885619
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Abstract: We present a rational version of the classical Landen transformation for elliptic integrals. 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.


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Additional Information

George Boros
Affiliation: Department of Mathematics, Xavier University, New Orleans, Louisiana 70125
Email: gboros@xula.math.edu

Victor H. Moll
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: vhm@math.tulane.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01347-3
PII: S 0025-5718(01)01347-3
Keywords: Rational functions, Landen transformation, integrals
Received by editor(s): April 27, 1999
Published electronically: November 9, 2001
Additional Notes: The second author was supported in part by NSF Grant DMS-0070567.
Article copyright: © Copyright 2001 American Mathematical Society