# Inline and display LaTeX math to PDF

Single dollar signs set math inline, double ones on its own line. The formulas are typeset as vector glyphs with proper spacing. Elsewhere they often arrive as blurry images or as the raw source.

$...$ inline and $$...$$ display math set as vector glyphs: fractions, radicals, sums, integrals, Greek letters, accents and styled alphabets. Toggle: math.

- PDF: https://legivel.com/examples/latex-math/inline-display-math.pdf
- Page: https://legivel.com/examples/latex-math/inline-display-math
- Open in the editor: https://legivel.com/markdown-to-pdf?sample=math
- More laTeX math in Markdown to PDF: https://legivel.com/examples/latex-math

## Markdown source

```markdown
# A formula sheet

Inline math sits on the baseline of the prose: the quadratic formula gives the roots of $ax^2 + bx + c = 0$ as $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, and a right triangle obeys $a^2 + b^2 = c^2$.

## Algebra

$$ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k} \qquad \binom{n}{k} = \frac{n!}{k!\,(n-k)!} $$

$$ \log_b(xy) = \log_b x + \log_b y \qquad a^{m} \cdot a^{n} = a^{m+n} \qquad \sqrt[n]{a^m} = a^{m/n} $$

## Trigonometry

$$ \sin^2\theta + \cos^2\theta = 1 \qquad \tan\theta = \frac{\sin\theta}{\cos\theta} \qquad \sin(\alpha \pm \beta) = \sin\alpha\cos\beta \pm \cos\alpha\sin\beta $$

The law of cosines, $c^2 = a^2 + b^2 - 2ab\cos\gamma$, reduces to Pythagoras when $\gamma = 90^\circ$.

## Calculus

$$ \frac{\mathrm{d}}{\mathrm{d}x} x^n = n x^{n-1} \qquad \int x^n \,\mathrm{d}x = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1) \qquad \int_a^b f(x)\,\mathrm{d}x = F(b) - F(a) $$

$$ e^{x} = \sum_{n=0}^{\infty} \frac{x^n}{n!} \qquad \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^{n} = e \qquad e^{i\pi} + 1 = 0 $$

## Series and the golden ratio

$$ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \qquad \varphi = \frac{1 + \sqrt{5}}{2} = 1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \cdots}}} $$

## Vectors, accents and alphabets

Vectors $\vec{v}$, unit vectors $\hat{\imath}$, means $\bar{x}$, time derivatives $\dot{x}$ and $\ddot{x}$, estimates $\hat{\theta}$, and the alphabets: $\mathbb{R}^n$, $\mathcal{L}$, $\mathfrak{g}$, $\mathbf{A}$, $\mathsf{T}$, $\mathtt{x}$.

$$ \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C} \qquad \mathbf{a} \cdot \mathbf{b} = \lVert \mathbf{a} \rVert \, \lVert \mathbf{b} \rVert \cos\theta \qquad \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \hat{\imath} & \hat{\jmath} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix} $$

Greek, upper and lower: $\alpha, \beta, \gamma, \delta, \epsilon, \varepsilon, \theta, \lambda, \mu, \pi, \sigma, \varphi, \omega$ and $\Gamma, \Delta, \Theta, \Lambda, \Pi, \Sigma, \Phi, \Omega$.
```