represents the sum of form[x] for all x that satisfy the polynomial equation f[x]==0.
- f must be a Function object such as (#^5-2#+1)&.
- form need not correspond to a polynomial function.
- Normal[expr] expands RootSum objects into explicit sums involving Root objects.
- f and form can contain symbolic parameters.
- RootSum[f,form] is automatically simplified whenever form is a rational function.
- RootSum is often generated in computing integrals of rational functions.
Examplesopen allclose all
Basic Examples (2)
Integrating a rational function of any order:
Automatic simplification of RootSum objects:
Compute a numerical approximation of a RootSum:
Evaluate to high precision:
Sums over roots of polynomials with inexact number coefficients:
Sums of numeric functions over roots of quadratics:
Sums of rational functions of roots:
Sums of logarithms of linear functions over roots of polynomials with rational coefficients:
Sums of numeric functions over roots of polynomials with multiple factors:
Represent a RootSum explicitly in terms of Root objects:
Integrate a rational function:
Sum a rational function:
Matrix exponential of any order:
Properties & Relations (2)
The residue theorem: