Markdown Math test1

This is the first paragraph.

$1(√𝜙√5−𝜙)𝑒25𝜋=1+𝑒−2𝜋1+𝑒−4𝜋1+𝑒−6𝜋1+𝑒−8𝜋1+⋯\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }$

Two mathematical blocks in a row

inline mathematics

This is an example for inline mathematics. When $𝐴 = 0 A=0$ and $𝑎 = 1 a=1$ then $𝐴 ≠𝑎A \neq a$ must be always true.

Examples from the mj3-demos

When $𝑎 ≠0a \ne 0$ , there are two solutions to $𝑎 𝑥 2 + 𝑏 𝑥 + 𝑐 = 0 ax^2 + bx + c = 0$ and they are

$𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎 x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

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

$(𝑛∑𝑘=1𝑎𝑘𝑏𝑘)2≤(𝑛∑𝑘=1𝑎2𝑘)(𝑛∑𝑘=1𝑏2𝑘)\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

$𝐕1×𝐕2=∣ ∣ ∣ ∣𝐢𝐣𝐤𝜕𝑋𝜕𝑢𝜕𝑌𝜕𝑢0𝜕𝑋𝜕𝑣𝜕𝑌𝜕𝑣0∣ ∣ ∣ ∣\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\ \end{vmatrix}$

$∇×⃗𝐁−1𝑐𝜕⃗𝐄𝜕𝑡=4𝜋𝑐⃗𝐣∇⋅⃗𝐄=4𝜋𝜌∇×⃗𝐄+1𝑐𝜕⃗𝐁𝜕𝑡=⃗𝟎∇⋅⃗𝐁=0\begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{align}$

Use non-standard symbols

To convert \bm you need to define a macro.

$𝒂=𝒃+𝒄\bm{a} = \bm{b} + \bm{c}$