Page 1

Displaying 1 – 16 of 16

Showing per page

A note on integration of rational functions

Jan Mařík (1991)

Mathematica Bohemica

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 ϕ with ϕ ' = P / Q n + 1 if and only if the Wronskian of the functions Q ' , ( Q 2 ) ' , ... , ( Q n ) ' , P is divisible by Q .

Introduction to Rational Functions

Christoph Schwarzweller (2012)

Formalized Mathematics

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

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

Introduction. The problem of determining the formula for P S ( n ) , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, h s , . . . , h s k , 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 x i n [(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

Omar Kihel, Jesse Larone (2015)

Acta Arithmetica

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.

Currently displaying 1 – 16 of 16

Page 1