This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# RootSum

 RootSumrepresents the sum of for all x that satisfy the polynomial equation .
• form need not correspond to a polynomial function.
• f and form can contain symbolic parameters.
• RootSum is automatically simplified whenever form is a rational function.
• RootSum is often generated in computing integrals of rational functions.
Integrating a rational function of any order:
Evaluate numerically:
Automatic simplification of RootSum objects:
Integrating a rational function of any order:
 Out[1]=
Evaluate numerically:
 Out[2]=

Automatic simplification of RootSum objects:
 Out[1]=
 Scope   (11)
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:
Derivatives:
Integrals:
Limits:
Series:
 Applications   (3)
Integrate a rational function:
Sum a rational function:
Matrix exponential of any order:
Vieta's formulas:
The residue theorem:
New in 3