single dollar . $ .

. double-dollar . $$ .

. single character inline equation. (valid=True) . $a$ .

. inline equation with single greek character (valid=True) . $\\varphi$ .

\\varphi

. simple equation starting and ending with numbers. (valid=True) . $1+1=2$ .

1+1=2

. simple equation including special html character. (valid=True) . $1+1<3$ .

1+1<3

. equation including backslashes. (valid=True) . $a \\backslash$ .

a \\backslash

. use of currency symbol, i.e. digits before/after opening/closing (valid=True) . 3$1+2$ $1+2$3 .

3$1+2$ $1+2$3

. use of currency symbol (valid=True) . If you solve $1+2$ you get $3 .

If you solve 1+2 you get $3

. inline fraction (valid=True) . $\\frac{1}{2}$ .

\\frac{1}{2}

. inline column vector (valid=True) . $\\begin{pmatrix}x\\\\y\\end{pmatrix}$ .

\\begin{pmatrix}x\\\\y\\end{pmatrix}

. inline bold vector notation (valid=True) . ${\\tilde\\bold e}_\\alpha$ .

{\\tilde\\bold e}_\\alpha

. exponentiation (valid=True) . $a^{b}$ .

a^{b}

. conjugate complex (valid=True) . $a^\*b$ with $a^\*$ .

a^\*b with a^\*

. Inline multi-line (valid=True) . a $a \not=1$ b .

a a \not=1 b

. Inline multi-line with newline (valid=False) . a $a \not=1$ b .

a $a

\not=1$ b

. single block equation, greek index (valid=True) . $$e_\\alpha$$ .

e_\\alpha

. display equation on its own single line. (valid=True) . $$1+1=2$$ .

1+1=2

. display equation with number on its own single line. (valid=True) . $$1+1=2$$ (2) .

¶ 1+1=2

. inline equation followed by block equation. (valid=True) . ${e}_x$ $$e_\\alpha$$ .

{e}_x

e_\\alpha

. underline tests (valid=True) . $$c{\\bold e}_x = a{\\bold e}_\\alpha - b\\tilde{\\bold e}_\\alpha$$ .

c{\\bold e}_x = a{\\bold e}_\\alpha - b\\tilde{\\bold e}_\\alpha

. non-numeric character before opening $ or after closing $ or both is allowed. (valid=True) . a$1+1=2$ $1+1=2$b c$x$d .

a1+1=2 1+1=2b cxd

. following dollar character '$' is allowed. (valid=True) . $x$ $ .

x $

. consecutive inline equations. (valid=True) . $x$ $y$ .

x y

. inline equation after '-' sign in text. (valid=True) . so-what is $x$ .

so-what is x

. display equation with line breaks. (valid=True) . $$ 1+1=2 $$ .

1+1=2

. multiple equations (valid=True) . $$ a = 1 $$ $$ b = 2 $$ .

a = 1

b = 2

. equation followed by a labelled equation (valid=True) . $$ a = 1 $$ $$ b = 2 $$ (1) .

a = 1

¶ b = 2

. multiline equation. (valid=True) . $$\\begin{matrix} f & = & 2 + x + 3 \\ & = & 5 + x \\end{matrix}$$ .

\\begin{matrix} f & = & 2 + x + 3 \\ & = & 5 + x \\end{matrix}

. vector equation. (valid=True) . $$\\begin{pmatrix}x_2 \\\\ y_2 \\end{pmatrix} = \\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix}\\cdot \\begin{pmatrix} x_1 \\\\ y_1 \\end{pmatrix}$$ .

\\begin{pmatrix}x_2 \\\\ y_2 \\end{pmatrix} = \\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix}\\cdot \\begin{pmatrix} x_1 \\\\ y_1 \\end{pmatrix}

. display equation with equation number. (valid=True) . $$f(x) = x^2 - 1$$ (1) .

¶ f(x) = x^2 - 1

. inline equation following code section. (valid=True) . `code`$a-b$ .

codea-b

. equation following code block. (valid=True) . ``` code ``` $$a+b$$ .

code

a+b

. numbered equation following code block. (valid=True) . ``` code ``` $$a+b$$(1) .

code

¶ a+b

. Equations in list. (valid=True) . 1. $1+2$ 2. $2+3$ 1. $3+4$ .

1+2
2+3
1. 3+4

. Inline sum. (valid=True) . $\\sum\_{i=1}^n$ .

\\sum\_{i=1}^n

. Sum without equation number. (valid=True) . $$\\sum\_{i=1}^n$$ .

\\sum\_{i=1}^n

. Sum with equation number. (valid=True) . $$\\sum\_{i=1}\^n$$ (2) .

¶ \\sum\_{i=1}\^n

. equation number always vertically aligned. (valid=True) . $${\\bold e}(\\varphi) = \\begin{pmatrix} \\cos\\varphi\\\\\\sin\\varphi \\end{pmatrix}$$ (3) .

¶ {\\bold e}(\\varphi) = \\begin{pmatrix} \\cos\\varphi\\\\\\sin\\varphi \\end{pmatrix}

. inline equations in blockquote. (valid=True) . > see $a = b + c$ > $c^2=a^2+b^2$ (2) > $c^2=a^2+b^2$ .

see a = b + c c^2=a^2+b^2 (2) c^2=a^2+b^2

. display equation in blockquote. (valid=True) . > formula > > $$ a+b=c$$ (2) > > in blockquote. .

formula

¶ a+b=c

in blockquote.

. mixed syntax: . $$ a=1 \\ b=2 $$ (abc) - ab $c=1$ d .

¶ a=1 \\ b=2

ab c=1 d

. escaped dollars '\\$' are interpreted as dollar '$' characters. (valid=True) . \\$1+1=2$ $1+1=2\\$ .

\1+1=2 1+1=2\\

. empty line between text and display formula is required. (valid=False) . some text \$\\$a+b=c\$\$ .

some text $\$a+b=c$$

. whitespace character after opening $ or before closing $ is not allowed. (valid=False) . $ $ $ x$ $x $ .

$ $ $ x$ $x $

. new line in blockquote block (valid=False): . > \$\$ a+b\n=c\$\$ .

$$ a+b\n=c$$

. math-escaping: escaped start $: . \$p_2 = $a .

$p_2 = $a

. math-escaping: escaped end $: . $p_2 = \$a .

$p_2 = $a

. math-escaping: internal escaped $: . $p_2 = \$1$ .

p_2 = \$1

. math-escaping: double-escaped start $: . \\$p_2 = 1$ .

\p_2 = 1

. math-escaping: double-escaped end $: . $p_2 = \\$a .

p_2 = \\a

. Inline double-dollar start: . $$a=1$$ b .

a=1

. Inline double-dollar end: . a $$a=1$$ .

a=1

. Inline double-dollar enclosed: . a $$a=1$$ (1) b .

a=1

(1) b

. Inline double-dollar, escaped: . a \$$a=1$$ b .

a $a=1$ b

. Inline mixed single/double dollars: . Hence, for $\alpha \in (0, 1)$, $$ \mathbb P (\alpha \bar{X} \ge \mu) \le \alpha; $$ i.e., $[\alpha \bar{X}, \infty)$ is a lower 1-sided $1-\alpha$ confidence bound for $\mu$. .

Hence, for \alpha \in (0, 1),

\mathbb P (\alpha \bar{X} \ge \mu) \le \alpha;

i.e., [\alpha \bar{X}, \infty) is a lower 1-sided 1-\alpha confidence bound for \mu.

. display equation with label containing whitespace. (valid=True) . $$1+1=2$$ (a b) .

¶ 1+1=2