# Symbols:E

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### Identity Element

$e$

Denotes the identity element in a general algebraic structure.

If $e$ is the identity of the structure $\struct {S, \circ}$, then a subscript is often used: $e_S$.

This is particularly common when more than one structure is under discussion.

The $\LaTeX$ code for $e_S$ is e_S .

### Euler's Number

$e$

Euler's number $e$ is the base of the natural logarithm $\ln$.

$e$ is defined to be the unique real number such that the value of the (real) exponential function $e^x$ has the same value as the slope of the tangent line to the graph of the function.

The $\LaTeX$ code for $e$ is e .

### Eccentricity

$e$

Used to denote the eccentricity of a conic section.

The $\LaTeX$ code for $e$ is e .

### exa-

$\mathrm E$

The Système Internationale d'Unités symbol for the metric scaling prefix exa, denoting $10^{\, 18 }$, is $\mathrm { E }$.

Its $\LaTeX$ code is \mathrm {E} .

$\mathrm E$ or $\mathrm e$

The hexadecimal digit $14$.

Its $\LaTeX$ code is \mathrm E  or \mathrm e.

### Duodecimal

$\mathrm E$

The duodecimal digit $11$.

Its $\LaTeX$ code is \mathrm E .

### Set

$E$

Used by some authors to denote a general set.

The $\LaTeX$ code for $E$ is E .

### Complete Elliptic Integral of the Second Kind

$\map E k$

$\ds \map E k = \int \limits_0^{\pi / 2} \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$

is the complete elliptic integral of the second kind, and is a function of $k$, defined on the interval $0 < k < 1$.

The $\LaTeX$ code for $\map E k$ is \map E k .

### Incomplete Elliptic Integral of the Second Kind

$\map E {k, \phi}$

$\ds \map E {k, \phi} = \int \limits_0^\phi \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$

is the incomplete elliptic integral of the second kind, and is a function of the variables:

$k$, defined on the interval $0 < k < 1$
$\phi$, defined on the interval $0 \le \phi \le \pi / 2$.

The $\LaTeX$ code for $\map E {k, \phi}$ is \map E {k, \phi} .

### Experiment

$\mathcal E$

An experiment, which can conveniently be denoted $\EE$, is a probability space $\struct {\Omega, \Sigma, \Pr}$.

The $\LaTeX$ code for $\mathcal E$ is \mathcal E  or \EE.

### Expectation

$\expect X$

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a real-valued discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.

The expectation of $X$, written $\expect X$, is defined as:

$\expect X := \ds \sum_{x \mathop \in \image X} x \map \Pr {X = x}$

whenever the sum is absolutely convergent, that is, when:

$\ds \sum_{x \mathop \in \image X} \size {x \map \Pr {X = x} } < \infty$

The $\LaTeX$ code for $\expect X$ is \expect X .

### Conditional Expectation

$\expect {X \mid B}$

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a discrete random variable on $\struct {\Omega, \Sigma, \Pr}$.

Let $B$ be an event in $\struct {\Omega, \Sigma, \Pr}$ such that $\map \Pr B > 0$.

The conditional expectation of $X$ given $B$ is written $\expect {X \mid B}$ and defined as:

$\expect {X \mid B} = \ds \sum_{x \mathop \in \image X} x \condprob {X = x} B$

where:

$\condprob {X = x} B$ denotes the conditional probability that $X = x$ given $B$

whenever this sum converges absolutely.

The $\LaTeX$ code for $\expect {X \mid B}$ is \expect {X \mid B} .

### Error Function

$\erf$

The error function is the following improper integral, considered as a real function $\erf : \R \to \R$:

$\map {\erf} x = \ds \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t$

where $\exp$ is the real exponential function.

Its $\LaTeX$ code is erf .

### Complementary Error Function

$\erfc$

The complementary error function is the real function $\erfc: \R \to \R$:

 $\ds \map {\erfc} x$ $=$ $\ds 1 - \map \erf x$ where $\erf$ denotes the Error Function $\ds$ $=$ $\ds 1 - \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t$ where $\exp$ denotes the Real Exponential Function $\ds$ $=$ $\ds \dfrac 2 {\sqrt \pi} \int_x^\infty \map \exp {-t^2} \rd t$

Its $\LaTeX$ code is erfc .

### East

$\mathrm E$

### East (Terrestrial)

East is the direction on (or near) Earth's surface along the small circle in the direction of Earth's rotation in space about its axis.

### East (Celestial)

The $\LaTeX$ code for $\mathrm E$ is \mathrm E .

### Energy

$E$

The usual symbol used to denote the energy of a body is $E$.

Its $\LaTeX$ code is E .

### Electric Field Strength

$\mathbf E$

The usual symbol used to denote electric field strength is $\mathbf E$.

Some sources use the calligraphic form $\EE$.

Its $\LaTeX$ code is \mathbf E .

### Electromotive Force

$\EE$

The usual symbol used to denote electromotive force is $\EE$.

Its $\LaTeX$ code is \EE .

### Elementary Charge

$\E$

The symbol used to denote the elementary charge is usually $\E$ or $e$.

The preferred symbol on $\mathsf{Pr} \infty \mathsf{fWiki}$ is $\E$.

Its $\LaTeX$ code is \E .

### Electrostatic Unit

$\mathrm {e.s.u.}$

The symbol for the electrostatic unit is $\mathrm {e.s.u.}$

Its $\LaTeX$ code is \mathrm {e.s.u.} .

### Electromagnetic Unit

$\mathrm {e.m.u.}$

The symbol for the electromagnetic unit is $\mathrm {e.m.u.}$

Its $\LaTeX$ code is \mathrm {e.m.u.} .

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