Symbols:Sigma

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.

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

Sum Notation

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 $S$.

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

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

Alternatively:

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

If $\Phi \left({j}\right)$ is a propositional function of $j$, then we can write:

$\displaystyle \sum_{\Phi \left({j}\right)} a_j = \text{ The sum of all } a_j \text{ such that } \Phi \left({j}\right) \text{ holds}$.

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

The $\LaTeX$ code for $\displaystyle \sum_{1 \le j \le n} a_j$ is \displaystyle \sum_{1 \le j \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 $n \ge 2$.

The sigma function $\sigma \left({n}\right)$ is defined on $n$ as being the sum of all the positive integer divisors of $n$.

That is:

$\displaystyle \sigma \left({n}\right) = \sum_{d \backslash n} d$

where $\displaystyle \sum_{d \backslash n}$ 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.

The $\LaTeX$ code for $\sigma$ is \sigma.

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:

$\displaystyle \sigma = \frac m A$

where:

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

The $\LaTeX$ code for $\sigma$ is \sigma.