Symbols:Lambda

Lambda

Von Mangoldt Function

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

The Von Mangoldt function (also known as the Mangoldt function) $\Lambda: \N \to \R$ is defined as:

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

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

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

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

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

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:

• $\operatorname{Im} \left({X}\right) = \left\{{0, 1, 2, \ldots}\right\} = \N$

• $\displaystyle \Pr \left({X = k}\right) = \frac 1 {k!} \lambda^k e^{-\lambda}$

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