Symbols:Greek/Gamma
Gamma
The $3$rd letter of the Greek alphabet.
- Minuscule: $\gamma$
- Majuscule: $\Gamma$
The $\LaTeX$ code for \(\gamma\) is \gamma .
The $\LaTeX$ code for \(\Gamma\) is \Gamma .
Gamma Function
- $\map \Gamma z$
The gamma function $\Gamma: \C \setminus \Z_{\le 0} \to \C$ is defined, for the open right half-plane, as:
- $\ds \map \Gamma z = \map {\MM \set {e^{-t} } } z = \int_0^{\to \infty} t^{z - 1} e^{-t} \rd t$
where $\MM$ is the Mellin transform.
For all other values of $z$ except the non-positive integers, $\map \Gamma z$ is defined as:
- $\map \Gamma {z + 1} = z \map \Gamma z$
The $\LaTeX$ code for \(\map \Gamma z\) is \map \Gamma z .
Euler-Mascheroni Constant
- $\gamma$
The Euler-Mascheroni constant $\gamma$ is the real number that is defined as:
| \(\ds \gamma\) | \(:=\) | \(\ds \lim_{n \mathop \to +\infty} \paren {\sum_{k \mathop = 1}^n \frac 1 k - \int_1^n \frac 1 x \rd x}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \lim_{n \mathop \to +\infty} \paren {H_n - \ln n}\) |
where $\sequence {H_n}$ are the harmonic numbers and $\ln$ is the natural logarithm.
Autocovariance
- $\gamma_k$
Let $S$ be a stochastic process giving rise to a time series $T$.
The autocovariance of $S$ at lag $k$ is defined as:
- $\gamma_k := \cov {z_t, z_{t + k} } = \expect {\paren {z_t - \mu} \paren {z_{t + k} - \mu} }$
where:
- $z_t$ is the observation at time $t$
- $\mu$ is the mean of $S$
- $\expect \cdot$ is the expectation.
Coefficient of Skewness
- $\gamma_1$
Let $X$ be a random variable with mean $\mu$ and standard deviation $\sigma$.
The coefficient of skewness of $X$ is the coefficient:
| \(\ds \gamma_1\) | \(=\) | \(\ds \dfrac {\mu_3} { {\mu_2}^{3/2} }\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \expect {\paren {\dfrac {X - \mu} \sigma}^3}\) |
where:
- $\mu_i$ denotes the $i$th central moment of $X$
- $\mu$ denotes the expectation of $X$, that is, its first central moment
- $\sigma$ denotes the standard deviation of $X$, that is, the square root of its second central moment.
Discount Factor
- $\gamma^n$
The symbol for a discount factor accumulated over $n$ conversion periods is $\gamma^n$.
The $\LaTeX$ code for \(\gamma^n\) is \gamma^n .
Gyromagnetic Ratio
- $\gamma$
The usual symbol used to denote gyromagnetic ratio is $\gamma$.
Its $\LaTeX$ code is \gamma .
Universal Gravitational Constant: Variant
- $\gamma$
The symbol for the universal gravitational constant can be presented as $\gamma$.
Its $\LaTeX$ code is \gamma .
Vacuum Permittivity: Variant
- $\Gamma_e$
Vacuum permittivity can also be seen denoted as $\Gamma_e$ in some older works.
The $\LaTeX$ code for \(\Gamma_e\) is \Gamma_e .
Vacuum Permeability: Variant
- $\Gamma_m$
Vacuum permeability can also be seen denoted as $\Gamma_m$ in some older works.
The $\LaTeX$ code for \(\Gamma_m\) is \Gamma_m .
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Appendix $1$: Symbols and Conventions: Greek Alphabet