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

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


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

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

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


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


Linear Density

$\lambda$

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

$\displaystyle \lambda = \frac m l$

where:


Parameter of Poisson Distribution

$\lambda$

Used to denote the parameter of a given Poisson distribution:


Let $X$ be a discrete random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.


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

  • $\operatorname{Im} \left({X}\right) = \left\{{0, 1, 2, \ldots}\right\} = \N$
  • $\displaystyle \Pr \left({X = k}\right) = \frac 1 {k!} \lambda^k e^{-\lambda}$


Left Regular Representation

$\lambda_a$

Let $\left ({S, \circ}\right)$ be an algebraic structure.


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

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


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


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