Geodesic
A note on integration of rational functions
Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 405-411

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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 $\varphi '=P/Q^{n+1}$ if and only if the Wronskian of the functions $Q',(Q^2)',\ldots,(Q^n)',P$ is divisible by $Q$.
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 $\varphi '=P/Q^{n+1}$ if and only if the Wronskian of the functions $Q',(Q^2)',\ldots,(Q^n)',P$ is divisible by $Q$.
DOI : 10.21136/MB.1991.126024
Classification : 26C15
Keywords: integration; primitive; rational function; Wronskian 
Mařík, Jan. A note on integration of rational functions. Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 405-411. doi: 10.21136/MB.1991.126024
@article{10_21136_MB_1991_126024,
     author = {Ma\v{r}{\'\i}k, Jan},
     title = {A note on integration of rational functions},
     journal = {Mathematica Bohemica},
     pages = {405--411},
     year = {1991},
     volume = {116},
     number = {4},
     doi = {10.21136/MB.1991.126024},
     mrnumber = {1146400},
     zbl = {0739.26012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1991.126024/}
}
TY  - JOUR
AU  - Mařík, Jan
TI  - A note on integration of rational functions
JO  - Mathematica Bohemica
PY  - 1991
SP  - 405
EP  - 411
VL  - 116
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1991.126024/
DO  - 10.21136/MB.1991.126024
LA  - en
ID  - 10_21136_MB_1991_126024
ER  - 
%0 Journal Article
%A Mařík, Jan
%T A note on integration of rational functions
%J Mathematica Bohemica
%D 1991
%P 405-411
%V 116
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1991.126024/
%R 10.21136/MB.1991.126024
%G en
%F 10_21136_MB_1991_126024

[1] G. H. Hardy: The integration of functions of a single variable. Second edition, Cambridge, 1928.

Cité par Sources :