MathML polyfill

Overview

This polyfill loads MathJax when MathML is detected on the page and the browser has inadequate MathML support.

Known issues

Browsers that lack MathML support (e.g. Chromium and IE11) will take longer to load MathML than browsers with MathML support
IE11 won't display MathML correctly in isolated networks. It relies on an extra polyfill that requires internet access.

Examples of simple formulas

Given the quadratic equation $a x^{2} + b x + c = 0$ , the roots are given by $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

Examples of complex formulas

Formula	Result
Bernoulli Trials	$P (E) Probability of event E: Get exactly k heads in n coin flips. = (\binom{n}{k}) Number of ways to get exactly k heads in n coin flips {p Probability of getting heads in one flip}_{}^{k Number of heads} {(1 - p) Probability of getting tails in one flip}_{}^{n - k Number of tails}$
Cauchy-Schwarz Inequality	${(\sum_{k = 1}^{n} a_{k}^{} b_{k}^{})}_{}^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})$
Cauchy Formula	$f (z) \cdot {Ind}_{γ}^{} (z) = \frac{1}{2 π i} \oint_{γ}^{} \frac{f (ξ)}{ξ - z} d ξ$
Cross Product	$V_{1}^{} \times V_{2}^{} = \| \begin{matrix} i & j & k \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{matrix} \|$
Vandermonde Determinant	$\| \begin{matrix} 1 & 1 & \dots & 1 \\ v_{1}^{} & v_{2}^{} & \dots & v_{n}^{} \\ v_{1}^{2} & v_{2}^{2} & \dots & v_{n}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ v_{1}^{n - 1} & v_{2}^{n - 1} & \dots & v_{n}^{n - 1} \end{matrix} \| = \prod_{1 \leq i < j \leq n}^{} (v_{j}^{} - v_{i}^{})$
Lorenz Equations	$\begin{array}{rcl} x_{}^{˙} & = & σ (y - x) \\ y_{}^{˙} & = & ρ x - y - x z \\ z_{}^{˙} & = & - β z + x y \end{array}$
Maxwell's Equations	${\begin{array}{rcl} \nabla \times B_{}^{↼} - \frac{1}{c} \frac{\partial E_{}^{↼}}{\partial t} & = & \frac{4 π}{c} j_{}^{↼} \\ \nabla \cdot E_{}^{↼} & = & 4 π ρ \\ \nabla \times E_{}^{↼} + \frac{1}{c} \frac{\partial B_{}^{↼}}{\partial t} & = & 0_{}^{↼} \\ \nabla \cdot B_{}^{↼} & = & 0 \end{array}$
Einstein Field Equations	$R_{μ ν}^{} - \frac{1}{2} g_{μ ν}^{} R = \frac{8 π G}{c_{}^{4}} T_{μ ν}^{}$
Ramanujan Identity	$\frac{1}{(\sqrt{φ \sqrt{5}} - φ) e_{}^{\frac{25}{π}}} = 1 + \frac{e_{}^{- 2 π}}{1 + \frac{e_{}^{- 4 π}}{1 + \frac{e_{}^{- 6 π}}{1 + \frac{e_{}^{- 8 π}}{1 + \dots}}}}$
Another Ramanujan identity	$\sum_{k = 1}^{\infty} \frac{1}{2_{}^{⌊ k \cdot φ ⌋}} = \frac{1}{2_{}^{0} + \frac{1}{2_{}^{1} + \dots \frac{1}{2_{}^{1} + \frac{1}{2_{}^{2} + \dots \frac{1}{2_{}^{3} + \frac{1}{2_{}^{5} + \dots}}}}}}$
Rogers-Ramanujan Identity	$1 + \sum_{k = 1}^{\infty} \frac{q_{}^{k_{}^{2} + k}}{(1 - q) (1 - q_{}^{2}) \dots (1 - q_{}^{k})} \frac{q_{}^{2}}{(1 - q)} + \frac{q_{}^{6}}{(1 - q) (1 - q_{}^{2})} + \dots = \prod_{j = 0}^{\infty} \frac{1}{(1 - q_{}^{5 j + 2}) (1 - q_{}^{5 j + 3})} \frac{1}{(1 - q_{}^{2}) (1 - q_{}^{3})} \times \frac{1}{(1 - q_{}^{7}) (1 - q_{}^{8})} \times \dots, for \| q \| < 1 .$

Date modified:: 2021-10-13