RootSum

RootSum[f,form]

represents the sum of form[x] for all x that satisfy the polynomial equation f[x]==0.

Details

  • 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.

Examples

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Basic Examples  (2)

Integrating a rational function of any order:

Evaluate numerically:

Automatic simplification of RootSum objects:

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:

Properties & Relations  (2)

Vieta's formulas:

The residue theorem:

Introduced in 1996
 (3.0)