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Partial Fraction Evaluation and Incomplete Decomposition of a Rational Function Whose Denominator Contains a Repeated Polynomial Factor

J. F. Mahoney
Mathematics of Computation
Vol. 44, No. 169 (Jan., 1985), pp. 167-175
DOI: 10.2307/2007800
Stable URL: http://www.jstor.org/stable/2007800
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Partial Fraction Evaluation and Incomplete Decomposition of a Rational Function Whose Denominator Contains a Repeated Polynomial Factor
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Abstract

Attention is directed to those proper rational functions whose denominators may be expressed as the product of an $N$th degree polynomial raised to the $K$th power and another polynomial of degree $M$. A method is presented for decomposing such a rational function into the sum of the $K$ partial fraction terms which proceed from the repeated polynomial plus a proper rational function which completes the equality. Use is made of an extended version of Horner's scheme. Two numerical examples and an operations count are presented. The method is free of complex arithmetic provided that all of the coefficients of the entering polynomials are real.

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