Markdown Math Formulas

LaTeX Math Formula Basics

In Markdown, mathematical formulas are represented using LaTeX syntax. LaTeX is a powerful typesetting system, especially suitable for documents containing complex mathematical formulas.

Basic Syntax Structure

  • Command: starting with a backslash\at the beginning, such as\alpha、\sum
  • Parameter: enclosed in curly braces{}such as\frac{a}{b}
  • Subscript: use_, such asx_1
  • Superscript: use^, such asx^2
  • Grouping: combining multiple characters with curly braces, such asx_{i+1}

Common LaTeX Commands

\alpha, \beta, \gamma  % 希腊字母
\sum, \prod, \int      % 求和、乘积、积分
\frac{分子}{分母}      % 分数
\sqrt{表达式}          % 平方根
\sqrt[n]{表达式}       % n次根

Inline Formulas and Block Formulas

Inline Formula

Inline formulas use a single dollar sign$to enclose; the formula is embedded in the text, e.g., the variable $x = 5$ and the function $f(x) = x^2 + 2x + 1$.

文本中的变量 $x = 5$ 和函数 $f(x) = x^2 + 2x + 1$。

Block Formula

Block formulas use double dollar signs$$to enclose; the formula is placed on its own line and centered:

E = mc^2

\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

$$E = mc^2$$

$$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$

Multi-line Formulas

Use thealignenvironment to create multi-line aligned formulas:


\begin{align}
f(x) &= ax^2 + bx + c \
f'(x) &= 2ax + b \
f''(x) &= 2a
\end{align}

$$
    \begin{align}
    f(x) &= ax^2 + bx + c \\
    f'(x)  &= 2ax + b \\
    f''(x)  &= 2a
    \end{align}
    $$

Common Mathematical Symbols

Basic Operation Symbols

  • Addition, subtraction, multiplication, division:+, -, \times, \div
  • Fractions:\frac{a}{b} → $\frac{a}{b}$
  • Square root:\sqrt{x}, \sqrt[n]{x} → $\sqrt{x}$, $\sqrt[n]{x}$
  • Exponents:x^2, e^{i\pi} → $x^2$, $e^{i\pi}$

Comparison Symbols

  • Equals:=, \neq, \equiv → $=$, $\neq$, $\equiv$
  • Greater than / less than:<, >, \leq, \geq → $<$, $>$, $\leq$, $\geq$
  • Approximately equal to:\approx, \sim → $\approx$, $\sim$

Set Symbols

  • Belongs to:\in, \notin → $\in$, $\notin$
  • Contains:\subset, \supset → $\subset$, $\supset$
  • Intersection and union:\cap, \cup → $\cap$, $\cup$
  • Empty set:\emptyset → $\emptyset$

Greek Letters

Common Greek letters and their LaTeX representations:

Lowercase Uppercase LaTeX Lowercase Uppercase LaTeX
α Α \alpha ν Ν \nu
β Β \beta ο Ο o
γ Γ \gamma π Π \pi
δ Δ \delta ρ Ρ \rho
ε Ε \epsilon σ Σ \sigma
θ Θ \theta τ Τ \tau
λ Λ \lambda φ Φ \phi
μ Μ \mu ω Ω \omega

Special Functions and Symbols

  • Trigonometric functions:\sin, \cos, \tan
  • Logarithms:\log, \ln
  • Limits:\lim_{x \to 0}
  • Summation:\sum_{i=1}^{n}
  • Integrals:\int_{a}^{b}
  • Infinity:\infty

Matrix Representation

Use thematrixenvironment:


\begin{pmatrix}
a & b \
c & d
\end{pmatrix}

$$
    \begin{pmatrix}
    a & b \\
    c & d
    \end{pmatrix}
    $$

Matrices with different bracket types:

  • pmatrix: parentheses $\begin{pmatrix} a & b \ c & d \end{pmatrix}$
  • bmatrix: square brackets $\begin{bmatrix} a & b \ c & d \end{bmatrix}$
  • vmatrix: determinant $\begin{vmatrix} a & b \ c & d \end{vmatrix}$
Other Extensions