# 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:

Wolfram Research (1996), RootSum, Wolfram Language function, https://reference.wolfram.com/language/ref/RootSum.html.

#### Text

Wolfram Research (1996), RootSum, Wolfram Language function, https://reference.wolfram.com/language/ref/RootSum.html.

#### CMS

Wolfram Language. 1996. "RootSum." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RootSum.html.

#### APA

Wolfram Language. (1996). RootSum. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootSum.html

#### BibTeX

@misc{reference.wolfram_2024_rootsum, author="Wolfram Research", title="{RootSum}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/RootSum.html}", note=[Accessed: 25-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_rootsum, organization={Wolfram Research}, title={RootSum}, year={1996}, url={https://reference.wolfram.com/language/ref/RootSum.html}, note=[Accessed: 25-June-2024 ]}