Symbols:Greek/Beta

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Beta

The $2$nd letter of the Greek alphabet.

Minuscule: $\beta$
Majuscule: $\Beta$

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

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

Beta Function

The Beta Function $\Beta: \C \times \C \to \C$ is defined for $\map \Re x, \map \Re y > 0$ as:

$\ds \map \Beta {x, y} := \int_{\mathop \to 0}^{\mathop \to 1} t^{x - 1} \paren {1 - t}^{y - 1} \rd t$

The $\LaTeX$ code for $\map \Beta {x, y}$ is \map \Beta {x, y} .

Celestial Latitude

$\beta$

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

The celestial latitude of $P$ is the angle subtended by the the arc of the vertical circle through $P$ between $P$ and the ecliptic.

If $P$ is closer to the north ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ north, where $\beta \degrees$ denotes $\beta$ degrees (of arc), written $\beta \degrees \, \mathrm N$.

If $P$ is closer to the south ecliptic pole, the celestial latitude is defined as latitude $\beta \degrees$ south, written $\beta \degrees \, \mathrm S$.

At the north ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm N$.

At the south ecliptic pole, the celestial latitude is $90 \degrees \, \mathrm S$.

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

Linguistic Note

The Greek letter $\Beta$, $\beta$ (beta) is properly pronounced bee-ta, not the frequently-heard hypercorrection bay-ta.

Sources

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