Rending math to HTML in R using katex
This vignette demonstrates some example math rendered server-side in R using the katex package. Refer to the upstream katex support table for the full list of supported tex functions.
Example equations from: https://www.intmath.com/cg5/katex-mathjax-comparison.php
Equation 1
<- " \\ 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} } } }" katex_html (tex1, include_css = TRUE )1 ( ϕ 5 − ϕ ) e 2 5 π ≡ 1 + e − 2 π 1 + e − 4 π 1 + e − 6 π 1 + e − 8 π 1 + ⋯ \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} } } } ( ϕ 5 − ϕ ) e 5 2 π 1 ≡ 1 + 1 + 1 + 1 + 1 + ⋯ e − 8 π e − 6 π e − 4 π e − 2 π
Equation 2
<- " \\ 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)" katex_html (tex2)( ∑ k = 1 n a k b k ) 2 ≤ ( ∑ k = 1 n a k 2 ) ( ∑ k = 1 n b k 2 ) \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) ( k = 1 ∑ n a k b k ) 2 ≤ ( k = 1 ∑ n a k 2 ) ( k = 1 ∑ n b k 2 )
Equation 3
<- "1 + \\ frac{q^2}{(1-q)}+ \\ frac{q^6}{(1-q)(1-q^2)}+ \\ cdots = \\ prod_{j=0}^{ \\ infty} \\ frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \\ text{ for } \\ lvert q \\ rvert < 1." katex_html (tex3)1 + q 2 ( 1 − q ) + q 6 ( 1 − q ) ( 1 − q 2 ) + ⋯ = ∏ j = 0 ∞ 1 ( 1 − q 5 j + 2 ) ( 1 − q 5 j + 3 ) , for ∣ q ∣ < 1. 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \text{ for }\lvert q\rvert < 1. 1 + ( 1 − q ) q 2 + ( 1 − q ) ( 1 − q 2 ) q 6 + ⋯ = j = 0 ∏ ∞ ( 1 − q 5 j + 2 ) ( 1 − q 5 j + 3 ) 1 , for ∣ q ∣ < 1.
Equation 4
<- " \\ int u \\ frac{dv}{dx} \\ ,dx=uv- \\ int \\ frac{du}{dx}v \\ ,dx" katex_html (tex4)∫ u d v d x d x = u v − ∫ d u d x v d x \int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx ∫ u d x d v d x = uv − ∫ d x d u v d x
Equation 5
<- "S ( \\ omega)= \\ frac{ \\ alpha g^2}{ \\ omega^5} \\ ,e ^{[-0.74 \\ bigl \\ { \\ frac{ \\ omega U_ \\ omega 19.5}{g} \\ bigr \\ }^{-4}]}" katex_html (tex5)S ( ω ) = α g 2 ω 5 e [ − 0.74 { ω U ω 19.5 g } − 4 ] S (\omega)=\frac{\alpha g^2}{\omega^5} \,e ^{[-0.74\bigl\{\frac{\omega U_\omega 19.5}{g}\bigr\}^{-4}]} S ( ω ) = ω 5 α g 2 e [ − 0.74 { g ω U ω 19.5 } − 4 ]
Equation 6
<- "f(n) = \\ begin{cases} \\ frac{n}{2}, & \\ text{if } n \\ text{ is even} \\\\ 3n+1, & \\ text{if } n \\ text{ is odd} \\ end{cases}" katex_html (tex6)f ( n ) = { n 2 , if n is even 3 n + 1 , if n is odd f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases} f ( n ) = { 2 n , 3 n + 1 , if n is even if n is odd
Equation 7
<- " \\ begin{aligned} \\ dot{x} & = \\ sigma(y-x) \\\\ \\ dot{y} & = \\ rho x - y - xz \\\\ \\ dot{z} & = - \\ beta z + xy \\ end{aligned}" katex_html (tex7)x ˙ = σ ( y − x ) y ˙ = ρ x − y − x z z ˙ = − β z + x y \begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned} x ˙ y ˙ z ˙ = σ ( y − x ) = ρ x − y − x z = − β z + x y
Equation 8
<- " \\ begin{pmatrix} a_{11} & a_{12} & a_{13} \\\\ a_{21} & a_{22} & a_{23} \\\\ a_{31} & a_{32} & a_{33} \\ end{pmatrix}" katex_html (tex8)( a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ) \begin{pmatrix}
a_{11} & a_{12} & a_{13}\\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33}
\end{pmatrix} ⎝ ⎛ a 11 a 21 a 31 a 12 a 22 a 32 a 13 a 23 a 33 ⎠ ⎞