A counterexample to the strong real Jocobian conjecture.
A factored form of complex analytic functions and its application to finding partial fraction decompositions.
A note on integration of rational functions
Let and be polynomials in one variable with complex coefficients and let be a natural number. Suppose that is not constant and has only simple roots. Then there is a rational function with if and only if the Wronskian of the functions is divisible by .
DCR2: An Improved Algorithm for l¶ Rational Approximation on Intervals.
Factorisation de fractions rationnelles et de suites récurrentes
Functions without residue and a bilinear differential equation
Introduction to Rational Functions
In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks
Itération des polynômes et propriétés d'orthogonalité
Markov and Bernstein type inequalities for polynomials.
On the power-series expansion of a rational function
Introduction. The problem of determining the formula for , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...
Prime rational functions
Let f(x) be a complex rational function. We study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we also derive some conditions for the case of complex polynomials.
Sur quelques théorèmes de M. Hermite extrait d'une lettre adressée à M. Borchardt.
Sur quelques théorèmes fondamentaux de l'algèbre moderne
Sur un théorème de G. Pólya.
Sur une formule d'Euler.
Systèmes dynamiques holomorphes