A note on integration of rational functions

Mathematica Bohemica (1991)

• Volume: 116, Issue: 4, page 405-411
• ISSN: 0862-7959

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Abstract

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Let $P$ and $Q$ be polynomials in one variable with complex coefficients and let $n$ be a natural number. Suppose that $Q$ is not constant and has only simple roots. Then there is a rational function $\varphi$ with ${\varphi }^{\text{'}}=P/{Q}^{n+1}$ if and only if the Wronskian of the functions ${Q}^{\text{'}},{\left({Q}^{2}\right)}^{\text{'}},...,{\left({Q}^{n}\right)}^{\text{'}},P$ is divisible by $Q$.

How to cite

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Mařík, Jan. "A note on integration of rational functions." Mathematica Bohemica 116.4 (1991): 405-411. <http://eudml.org/doc/29178>.

@article{Mařík1991,
abstract = {Let $P$ and $Q$ be polynomials in one variable with complex coefficients and let $n$ be a natural number. Suppose that $Q$ is not constant and has only simple roots. Then there is a rational function $\varphi$ with $\varphi ^\{\prime \}=P/Q^\{n+1\}$ if and only if the Wronskian of the functions $Q^\{\prime \},(Q^2)^\{\prime \},\ldots ,(Q^n)^\{\prime \},P$ is divisible by $Q$.},
author = {Mařík, Jan},
journal = {Mathematica Bohemica},
keywords = {integration; primitive; rational function; Wronskian; integration; primitive; rational function; Wronskian},
language = {eng},
number = {4},
pages = {405-411},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on integration of rational functions},
url = {http://eudml.org/doc/29178},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Mařík, Jan
TI - A note on integration of rational functions
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 4
SP - 405
EP - 411
AB - Let $P$ and $Q$ be polynomials in one variable with complex coefficients and let $n$ be a natural number. Suppose that $Q$ is not constant and has only simple roots. Then there is a rational function $\varphi$ with $\varphi ^{\prime }=P/Q^{n+1}$ if and only if the Wronskian of the functions $Q^{\prime },(Q^2)^{\prime },\ldots ,(Q^n)^{\prime },P$ is divisible by $Q$.
LA - eng
KW - integration; primitive; rational function; Wronskian; integration; primitive; rational function; Wronskian
UR - http://eudml.org/doc/29178
ER -

References

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1. G. H. Hardy, The integration of functions of a single variable, Second edition, Cambridge, 1928. (1928)

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