Complete LaTeX Delimiter Test Article

This article tests all supported LaTeX delimiter formats in our markdown renderer.

1. Standard LaTeX Delimiters (backslash-bracket format)

Display Math with

$$...$$

Here's a complex function with proper \[...\] delimiters:

$$F(x) = \frac{d}{dx}\left[ e^{x^{2}} \int_{0}^{x} \frac{\sin(t^{3}) + \ln(1+t^{2})}{1+t^{4}}\, dt \right]$$

Another example with summation:

$$\sum_{n=1}^{\infty} \frac{(-1)^n}{n^2}\cos\bigl(nx^2 + \sqrt{n}\bigr)$$

And a limit with product:

$$\lim_{N\to\infty}\prod_{k=1}^{N}\left(1 + \frac{x^2}{k^2}e^{-x/k}\right)$$

Inline Math with $...$

This is inline math using backslash-parentheses: the function $F(x)$ is defined using $e^{x^{2}}$ which appears in the integral. We also have $\sin(t^3)$ and $\ln(1+t^2)$ in the numerator.

More inline examples: $\alpha + \beta = \gamma$ and $\int_{0}^{\infty} e^{-x} dx = 1$.

2. Dollar Sign Delimiters

Display Math with $...$

Using double dollar signs for display math:

$$G(x) = \int_{-\infty}^{\infty} e^{-x^2} \cdot \sin(x) \, dx$$

Another example:

$\frac{d^2y}{dx^2} + \omega^2 y = 0$

Inline Math with $...$

Using single dollar signs for inline: $e^{i\pi} + 1 = 0$ is Euler's identity. Also $\sqrt{2}$ is irrational and $\pi \approx 3.14159$.

3. Plain Bracket Format (multiline)

Format 1: Brackets on separate lines

$$\frac{d}{dx}\left[e^{x^2}\int_{0}^{x} \frac{\sin(t^3)+\ln(1+t^2)}{1+t^4},dt\right]$$

Another with summation:

$$\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}$$

Format 2: Brackets on same line with content

Content before the math.

$$\int_{0}^{1} x^n \, dx = \frac{1}{n+1}$$

Content after the math.

4. Mixed Content Test

Let's test a real mathematical explanation mixing all formats:

Consider the differential equation $\frac{dy}{dx} = y$. The general solution is $y = Ce^x$ where $C$ is a constant.

The Fourier series of a periodic function $f(x)$ is:

$$f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty}\left(a_n\cos(nx) + b_n\sin(nx)\right)$$

Where the coefficients are calculated using:

$a_n = \frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(nx)\,dx$

And similarly for $b_n$.

5. Complex Expression with Inline Parentheses

The function $(F(x))$ is complicated. It uses $(e^{x^2})$ and has terms like $(\alpha + \beta)$. Don't confuse regular parentheses with math delimiters.

Regular text with (parentheses) should not be treated as math, but $\sin(x)$ should be.

6. Edge Cases

Empty or minimal expressions

Inline: $x$ and display:

$$y$$

Also: $a$ and $b$

Multiple expressions on one line

We have $\alpha$, $\beta$, and $\gamma$ all inline. Similarly $x$, $y$, and $z$.

Nested delimiters

$$\left\{ x \in \mathbb{R} : \left| x - \mu \right| < \sigma \right\}$$

And: $\left[\frac{a}{b}\right]$ with brackets inside.

Summary

This article tests:

1. ✓ \[...\] display math
2. ✓ \(...\) inline math
3. ✓ $$...$$ display math
4. ✓ $...$ inline math
5. ✓ [\n...\n] plain bracket multiline
6. ✓ Mixed formats in same document

If all these render correctly, the LaTeX parser is working properly!