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KaTeX and MathJax Comparison Demo

Page by Murray Bourne, IntMath.com. Last updated: 29 Apr 2020

Repeating fractions

1(ϕ5−ϕ)e25π1+e−2π1+e−4π1+e−6π1+e−8π1+⋯\displaystyle \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }

Summation notation

(∑k=1nakbk)2≤(∑k=1nak2)(∑k=1nbk2)\displaystyle \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)

Inline math

And here is some in-line math: kn+1=n2+kn2−kn−1k_{n+1} = n^2 + k_n^2 - k_{n-1}, followed by some more text.

Calculus

∫udvdxdx=uv−∫dudxvdx\displaystyle \int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx

Lorenz Equations

x˙=σ(y−x)y˙=ρx−y−xzz˙=−βz+xy\displaystyle \begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}

Case definitions

f(n)={n2,if n is even3n+1,if n is odd\displaystyle f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases}

Matrices

(a11a12a13a21a22a23a31a32a33)\displaystyle \begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}