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Formula Library

Browse formulas verified across both dialects. Every preview is rendered by the same Go engine that powers the playground.

60 formulas 11 categories Rendering previews…
Algebra tex / inline

Absolute

\left|x-y\right|
Algebra tex / display

Binomial

\binom{n}{k}
Algebra tex / inline

Exponents

\left(\frac{x^2y^{-3}}{z^4}\right)^2=\frac{x^4}{y^6z^8}
Algebra tex / inline

Fraction

\frac{a+b}{2}
Algebra tex / display

Logarithms

\log_b(xy)=\log_b x+\log_b y
Algebra tex / display

Nth Root

\sqrt[3]{x+1}+\sqrt{x^2+1}
Algebra tex / display

Quadratic

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
Algebra tex / inline

Radical

\sqrt{x^2+y^2}
Calculus tex / display

Contour Integral

\oint_C\vec F\cdot d\vec r
Calculus tex / inline

Derivative

f'(x)
Calculus tex / display

Gaussian Integral

\int_0^\infty e^{-x^2}\,dx=\frac{\sqrt{\pi}}{2}
Calculus tex / display

Integral

\int_0^1x^2\,dx=\frac{1}{3}
Calculus tex / display

Limit

\lim_{x\to0}\frac{\sin x}{x}=1
Calculus tex / display

Partial

\frac{\partial f}{\partial x}
Calculus tex / display

Product

\prod_{k=1}^{n}k=n!
Calculus tex / display

Sum

\sum_{i=1}^{n}i=\frac{n(n+1)}{2}
Calculus tex / display

Taylor Series

f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n
Delimiters tex / display

Explicit

\Bigl(\frac{a}{b}\Bigr)
Delimiters tex / inline

Floor

\lfloor x\rfloor+\lceil y\rceil
Delimiters tex / inline

Norm

\|\mathbf v\|\le |x|+|y|
Delimiters tex / display

Paired

\left(\frac{a}{b}\right)
Equation Tags tex / display

Align End

x\tag{1}
Equation Tags tex / display

Constrained

a+b+c+d+e+f\tag{1}
Equation Tags tex / display

Free

x\tag{1}
Linear Algebra tex / inline

Determinant

\det(A)
Linear Algebra tex / display

Eigen

A\mathbf{x}=\lambda\mathbf{x}
Linear Algebra tex / display

Inverse

A^{-1}=\frac{1}{\det A}\operatorname{adj}A
Linear Algebra tex / display

Matrix

\begin{pmatrix}1&2\\3&4\end{pmatrix}
Linear Algebra tex / inline

Transpose

A^T B^T
Linear Algebra tex / display

Vandermonde

\det\begin{pmatrix}1&x&x^2\\1&y&y^2\\1&z&z^2\end{pmatrix}=(x-y)(y-z)(z-x)
Linear Algebra tex / display

Vector

\vec v=(1,2,3)
Multiline tex / display

Aligned

\begin{aligned}x&=1\\y&=2\end{aligned}
Multiline tex / display

Alignenv

\begin{align*}a&=b\\c&=d\end{align*}
Multiline tex / display

Cases

f(x)=\begin{cases}x^2,&x\ge0\\-x,&x<0\end{cases}
Multiline tex / display

Gathered

\begin{gathered}a=b+c\\d=e+f\end{gathered}
Physics & Engineering tex / display

Coulomb

F=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2}
Physics & Engineering tex / inline

Force

\mathbf{F}=m\mathbf{a}
Physics & Engineering tex / display

Gravitation

F=G\frac{m_1m_2}{r^2}
Physics & Engineering tex / display

Maxwell

\nabla\cdot\mathbf{E}=\frac{\rho}{\varepsilon_0}
Physics & Engineering tex / display

Schrodinger

i\hbar\frac{\partial}{\partial t}\Psi=\hat H\Psi
Physics & Engineering tex / display

Units

9.81\,\mathrm{m/s^2}
Physics & Engineering tex / display

Wave

\frac{\partial^2u}{\partial t^2}=c^2\nabla^2u
Probability & Statistics tex / display

Bayes

P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}
Probability & Statistics tex / display

Binomial

P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}
Probability & Statistics tex / inline

Conditional

P(A\mid B)=\frac{P(A\cap B)}{P(B)}
Probability & Statistics tex / display

Expectation

\mathbb{E}[X]=\sum_x xP(X=x)
Probability & Statistics tex / display

Normal

f(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}
Probability & Statistics tex / inline

Variance

\operatorname{Var}(X)=\mathbb{E}[X^2]-(\mathbb{E}[X])^2
Sets & Logic tex / display

De Morgan

\neg(A\land B)=\neg A\lor\neg B
Sets & Logic tex / inline

Forall

\forall x\in\mathbb{R},\ x^2\ge0
Sets & Logic tex / display

Implication

(p\land q)\to r
Sets & Logic tex / inline

Map

f:X\to Y
Sets & Logic tex / inline

Subsets

A\subseteq B\iff A\cup B=B
Sets & Logic tex / display

Union

A\cup B=\{x\mid x\in A\text{ or }x\in B\}
Text & Fallback tex / inline

English

x>0\text{ if and only if }x\in\mathbb{R}
Display Wrapping tex / display

Center

a+b+c+d+e+f+g+h+i+j
Display Wrapping tex / display

End

a+b+c+d+e+f+g+h+i+j
Display Wrapping tex / display

Display

a+b+c+d+e+f+g+h+i+j
Display Wrapping tex / display

Overfull

\frac{a+b}{c+d}
Display Wrapping tex / display

Zero Width Break

a\allowbreak\vphantom{X}b+c+d