Symbols:Greek/Lambda

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Lambda

The $11$th letter of the Greek alphabet.

Minuscule: $\lambda$
Majuscule: $\Lambda$

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

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


Von Mangoldt Function

$\map \Lambda n$


The von Mangoldt function $\Lambda: \N \to \R$ is defined as:

$\map \Lambda n = \begin{cases} \map \ln p & : \exists m \in \N, p \in \mathbb P: n = p^m \\ 0 & : \text{otherwise} \end{cases}$

where $\mathbb P$ is the set of all prime numbers.


The $\LaTeX$ code for \(\map \Lambda n\) is \map \Lambda n .


Triangle Function

$\map \Lambda x$


The triangle function is the real function $\Lambda: \R \to \R$ defined as:

$\forall x \in \R: \map \Lambda x := \begin {cases} 1 - \size x : & \size x \le 1 \\ 0 : & \size x > 1 \end {cases}$

where $\size x$ denotes the absolute value function.


The $\LaTeX$ code for \(\map \Lambda x\) is \map \Lambda x .


Linear Mass Density

$\lambda$

Used to denote the linear mass density of a given one-dimensional body:

$\lambda = \dfrac m l$

where:

$m$ is the body's mass
$l$ is the body's length.


Poisson Distribution

$\lambda$

Used to denote the parameter of a given Poisson distribution:


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


Then $X$ has the Poisson distribution with parameter $\lambda$ (where $\lambda > 0$) if and only if:

$\Img X = \set {0, 1, 2, \ldots} = \N$
$\map \Pr {X = k} = \dfrac 1 {k!} \lambda^k e^{-\lambda}$


It is written:

$X \sim \Poisson \lambda$


Order Type of Real Numbers

$\lambda$

The order type of $\struct {\R, \le}$ is denoted $\lambda$ (lambda).


Left Regular Representation

$\lambda_a$

Let $\struct {S, \circ}$ be an algebraic structure.


The mapping $\lambda_a: S \to S$ is defined as:

$\forall x \in S: \map {\lambda_a} x = a \circ x$


This is known as the left regular representation of $\struct {S, \circ}$ with respect to $a$.


The $\LaTeX$ code for \(\map {\lambda_a} x\) is \map {\lambda_a} x .


Celestial Longitude

$\lambda$

Let $P$ be a point on the celestial sphere.

Let $J$ be a great circle on the celestial sphere passing through $P$ and both of the north ecliptic pole and south ecliptic pole.

The celestial longitude $\lambda$ of $P$ is the (spherical) angle (measuring east) that $J$ makes with the vernal equinox.

It ranges from $0$ to $360 \degrees$.


Compton Wavelength

$\lambda$

The symbol for the Compton wavelength is $\lambda$.

For specific particles, the symbol denoting that particle can be added as a subscript.


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


Compton Wavelength: Variant

$\lambda_{\mathrm C}$

Some sources present the symbol for the Compton wavelength as $\lambda_{\mathrm C}$.

For specific particles, the symbol denoting that particle can then be included with the subscripted $\mathrm C$, separated with a comma.


The $\LaTeX$ code for \(\lambda_{\mathrm C}\) is \lambda_{\mathrm C} .


Compton Wavelength of Electron

$\lambda_\E$

The symbol for the Compton wavelength of the electron is $\lambda_\E$.


The $\LaTeX$ code for \(\lambda_\E\) is \lambda_\E .


Compton Wavelength of Electron: Variant

$\lambda_{\mathrm C}$

Some sources present the symbol for the Compton wavelength of the electron as $\lambda_{\mathrm C}$.


The $\LaTeX$ code for \(\lambda_{\mathrm C}\) is \lambda_{\mathrm C} .


Compton Wavelength of Proton

$\lambda_{\mathrm p}$

The symbol for the Compton wavelength of the proton is $\lambda_{\mathrm p}$.


The $\LaTeX$ code for \(\lambda_{\mathrm p}\) is \lambda_{\mathrm p} .


Compton Wavelength of Proton: Variant

$\lambda_{\mathrm {C, p} }$

Some sources present the symbol for the Compton wavelength of the Proton as $\lambda_{\mathrm {C, p} }$.


The $\LaTeX$ code for \(\lambda_{\mathrm {C, p} }\) is \lambda_{\mathrm {C, p} } .


Reduced Compton Wavelength

$\lambdabar$

The symbol for the reduced Compton wavelength is $\lambdabar$.

For specific particles, the symbol denoting that particle can be added as a subscript.


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


Reduced Compton Wavelength: Variant

$\overline \lambda$

The conventional symbol $\lambdabar$ for the reduced Compton wavelength does not render particularly effectively.

Hence some sources present the symbol for the Compton wavelength as $\overline \lambda$.

For specific particles, the symbol denoting that particle can then be included with a subscript.


The $\LaTeX$ code for \(\overline \lambda\) is \overline \lambda .


Reduced Compton Wavelength of Electron

$\lambdabar_\E$

The symbol for the reduced Compton wavelength of the electron is $\lambdabar_\E$.


The $\LaTeX$ code for \(\lambdabar_\E\) is \lambdabar_\E .


Reduced Compton Wavelength of Electron: Variant

$\overline {\lambda_\E}$

Some sources present the symbol for the reduced Compton wavelength of the electron as $\overline {\lambda_\E}$.


The $\LaTeX$ code for \(\overline {\lambda_\E}\) is \overline {\lambda_\E} .


Reduced Compton Wavelength of Proton

$\lambdabar_{\mathrm p}$

The symbol for the reduced Compton wavelength of the proton is $\lambdabar_{\mathrm p}$.


The $\LaTeX$ code for \(\lambdabar_{\mathrm p}\) is \lambdabar_{\mathrm p} .


Reduced Compton Wavelength of Proton: Variant

$\overline {\lambda_{\mathrm p} }$

Some sources present the symbol for the reduced Compton wavelength of the proton as $\overline {\lambda_{\mathrm p} }$.


The $\LaTeX$ code for \(\overline {\lambda_{\mathrm p} }\) is \overline {\lambda_{\mathrm p} } .


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