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
tex1 <- "\\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
tex2 <- "\\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
tex3 <- "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
tex4 <- "\\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
tex5 <- "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
tex6 <- "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
tex7 <- "\\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
tex8 <- "\\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