A practical reference for the most commonly used formula constructs. Most formulas are built from combinations of these basic elements.
Powers and Subscripts
$$x^2 \quad x^{10} \quad x^{n+1}$$$$x_i \quad x_{n-1} \quad a_{ij}$$$$x_i^2 \quad \sum_{i=0}^{n}$$If the argument is more than one character, always wrap it in
{}:x^{n+1}, notx^n+1.
Fractions
$$\frac{a}{b} \quad \frac{x+1}{x-1} \quad \frac{d}{dx}f(x)$$Nested fractions:
$$\frac{1}{1 + \frac{1}{x}}$$For inline use, fractions render more compactly with \tfrac{}{} (text-style fraction):
Average: $\tfrac{a+b}{2}$
Roots
Square root:
$$\sqrt{x} \quad \sqrt{x^2 + y^2}$$nth root:
$$\sqrt[3]{8} = 2 \quad \sqrt[n]{a^n} = a$$
Greek Letters
Lowercase
| Code | Symbol | Code | Symbol |
|---|---|---|---|
\alpha | α | \nu | ν |
\beta | β | \xi | ξ |
\gamma | γ | \pi | π |
\delta | δ | \rho | ρ |
\epsilon | ε | \sigma | σ |
\zeta | ζ | \tau | τ |
\eta | η | \phi | φ |
\theta | θ | \chi | χ |
\lambda | λ | \psi | ψ |
\mu | μ | \omega | ω |
Uppercase
$$\Gamma \quad \Delta \quad \Theta \quad \Lambda \quad \Pi \quad \Sigma \quad \Phi \quad \Psi \quad \Omega$$Usage example:
$$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}$$
Arithmetic Operators
$$a + b - c \times d \div e$$$$a \cdot b \quad a \circ b \quad a \ast b$$$$\pm a \quad \mp a$$Comparison Operators
$$a < b \quad a > b \quad a \leq b \quad a \geq b$$$$a \neq b \quad a \approx b \quad a \equiv b$$$$a \ll b \quad a \gg b$$
Special Symbols
Infinity and limits notation
$$x \to \infty \quad x \to -\infty \quad x \to 0^+$$Sets
$$\in \quad \notin \quad \subset \quad \subseteq \quad \cup \quad \cap \quad \emptyset$$Example:
$$x \in \mathbb{R}, \quad x \in [0, 1)$$Arrows
$$\to \quad \leftarrow \quad \leftrightarrow \quad \Rightarrow \quad \Leftrightarrow$$Brackets
Brackets automatically scale to match their content using \left and \right:
$$\left( \frac{x}{y} \right)^2$$$$\left[ \frac{a+b}{c-d} \right]$$$$\left\{ x \in \mathbb{R} \mid x > 0 \right\}$$$$\left\langle v, w \right\rangle$$$$\left| x \right| \quad \left\| x \right\|$$Always use
\leftand\rightin pairs — otherwise the formula will not compile.
Text Inside Formulas
$$f(x) = x^2 \quad \text{for } x \geq 0$$$$\text{Lead Time} = \text{Done Date} - \text{Start Date}$$Practical Examples
Bayes’ Theorem
$$P(A \mid B) = \frac{P(B \mid A)\, P(A)}{P(B)}$$Standard Deviation
$$\sigma = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \bar{x})^2}{N}}$$Team Velocity
$$v = \frac{\text{story points}}{\text{sprint days}}$$Percentile (p95)
$$p_{95} = \text{sort}(t)[\lfloor 0.95 \cdot N \rfloor]$$