LaTeX Examples

Resource: http://en.wikibooks.org/wiki/LaTeX/Mathematics

$\frac{a+b}{c \div d}$ $a \div b$ $$ a / b $$ $\frac{a}{b}$ $a \times b$ $a \cdot b$ $x \div y \times z$ $x \div y z$ $(x \div y) \times z$ $$ y z $$ $x \div y \cdot z$ $x \div y \div z$ $x \div y / z$ $x + a \div y + b$ $$ x + a/y + b $$

$x \div y \times z$ $x \div y \cdot z$ $x \div y z$

$x / y \times z$ $x / y \cdot z$ $$ x / y z $$

$$ x y $$ $x \times y$ $$ 3 y $$ $$ x 3 $$ $$ 3 4 $$ $x \times 3$ $3 \times 4$

$\sin n \times \cos m$ $(\sin n) \times (\cos m)$ $\sin n \times \pi$ $\sin (n \times \pi)$

Notation as a Tool of Thought, Figure 3.

$\sum_{j=1}^{n} j \cdot 2^{-j}$

$1 \cdot 2 \cdot 3 + 2 \cdot 3 \cdot 4 + \dots \textit{n terms} \leftrightarrow \frac{1}{4} n (n+1) (n+2) (n+3)$

$1 \cdot 2 \cdot 3 \cdot 4 + 2 \cdot 3 \cdot 4 \cdot 5 + \dots \textit{n terms} \leftrightarrow \frac{1}{5} n (n+1) (n+2) (n+3) (n+4)$

$\frac{[\frac{x-a}{N}]^{-q}}{\Gamma(-q)}\sum_{j=0}^{N-1} \frac{\Gamma(j-q)}{\Gamma(j+1)} f\bigg(x- j \bigg[\frac{x-a}{N}\bigg] \bigg)$

$x \bmod y = x - y \lfloor x/y \rfloor, \ \ \ \ for \ y \ne 0.$

Let $P$ be the set of primes $p$ such that $p^2\leq n$ , and let $m=\left| P\right|$ . Then the number of semiprimes less than or equal to $n$ is given by
$\sum_{p\in P} \left(\pi(n/p)-\pi(p)\right)=\sum_{p\in P} \pi(n/p)- \frac{m(m-1)}2$

Something is still amiss in the formula. For

$\sum_{p\in P} \left(\pi(n/p)-\pi(p)\right)=\sum_{p\in P} \pi(n/p)- \frac{m(m-1)}2$

to be true, it must be that

$\sum_{p\in P}\pi(p)=\frac{m(m-1)}2$

$\sum_{i=0}^n a_i x^i$

$++/ (M=\iota^1 \,\, {}_+^\circ \,\, \iota^1) // M$

$+/ (M=\iota^1(\mu(M)) \,\, {}_+^\circ \,\, \iota^1(\nu(M))) / M$

$\iota^k(n)$	`k`-origin indexing; `k+i.n` in J
${}_+^\circ$	outer product; the dyad `+/` in J
$\mu(M)$	the number of rows in matrix ; `#M` in J
$\nu(M)$	the number of columns in matrix ; `{:$M` in J
	equivalent to `,B#"1 M` in J
	equivalent to `,B#"1&\|:M` in J

The formula $\sqrt{l^2 + w^2}$ computes the diagonal of a rectangle with sides $$l$$ and $$w$$

RogerHui/LaTeX_Examples

LaTeX Examples