Built-in Mathematica Symbol

RootSum

RootSum[f, form]
represents the sum of form[x] for all x that satisfy the polynomial equation f[x]

0.

RootSum[f, form] is automatically simplified whenever form is a rational function.

Integrating a rational function of any order:

Evaluate numerically:

Automatic simplification of RootSum objects:

Integrating a rational function of any order:

Evaluate numerically:

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:

Derivatives:

Integrals:

Limits:

Series:

Integrate a rational function:

Sum a rational function:

Matrix exponential of any order:

Vieta's formulas:

The residue theorem: