Symbols:Greek/Sigma

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Sigma

The $18$th letter of the Greek alphabet.

Minuscules: $\sigma$ and $\varsigma$

Majuscule: $\Sigma$

The $\LaTeX$ code for \(\sigma\) is \sigma .
The $\LaTeX$ code for \(\varsigma\) is \varsigma .

The $\LaTeX$ code for \(\Sigma\) is \Sigma .

Event Space

$\Sigma$

Let $\mathcal E$ be an experiment.

The event space of $\mathcal E$ is usually denoted $\Sigma$ (Greek capital sigma), and is the set of all outcomes of $\mathcal E$ which are interesting.

Summation

Let $\left({S, +}\right)$ be an algebraic structure where the operation $+$ is an operation derived from, or arising from, the addition operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.

The composite is called the summation of $\left({a_1, a_2, \ldots, a_n}\right)$, and is written:

$\displaystyle \sum_{j \mathop = 1}^n a_j = \left({a_1 + a_2 + \cdots + a_n}\right)$

The $\LaTeX$ code for \(\displaystyle \sum_{j \mathop = 1}^n a_j\) is \displaystyle \sum_{j \mathop = 1}^n a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j\) is \displaystyle \sum_{1 \mathop \le j \mathop \le n} a_j .

The $\LaTeX$ code for \(\displaystyle \sum_{\Phi \left({j}\right)} a_j\) is \displaystyle \sum_{\Phi \left({j}\right)} a_j .

Sigma Function

$\sigma \left({n}\right)$

Let $n$ be an integer such that $n \ge 1$.

The sigma function $\map \sigma n$ is defined on $n$ as being the sum of all the positive integer divisors of $n$.

That is:

$\displaystyle \map \sigma n = \sum_{d \mathop \divides n} d$

where $\displaystyle \sum_{d \mathop \divides n}$ is the sum over all divisors of $n$.

The $\LaTeX$ code for \(\sigma \left({n}\right)\) is \sigma \left({n}\right) .

Surface Charge Density

$\sigma$

Used to denote the surface charge density of a given body:

$\displaystyle \sigma = \frac q A$

where:

• $q$ is the body's electric charge;
• $A$ is the body's area.

Area Density

$\sigma$

Used sometimes, although $\rho_A$ (Greek letter rho) is more common, to denote the area density of a given two-dimensional body:

$\sigma = \dfrac m A$

where:

• $m$ is the body's mass;
• $A$ is the body's area.