Elementary symmetric sum

A symmetric sum is a type of summation.

Definition

The $k$ -th symmetric sum of a set of $n$ numbers is the sum of all products of $k$ of those numbers ( $1 \leq k \leq n$ ). For example, if $n = 4$ , and our set of numbers is $\{a, b, c, d\}$ , then:

1st Symmetric Sum = $a+b+c+d$

2nd Symmetric Sum = $ab+ac+ad+bc+bd+cd$

3rd Symmetric Sum = $abc+abd+acd+bcd$

4th Symmetric Sum = $abcd$

Notation

The first symmetric sum of $f(x)$ is often written $\sum_{sym}f(x)$ . The $n$ th can be written $\sum_{sym}^{n}f(x)$

Uses

Symmetric sums show up in Vieta's formulas

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Elementary symmetric sum

Contents

Definition

Notation

Uses

See Also