Continued fractions
\[ \begin{equation} x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + a_4}}} \end{equation} \]
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ASCIIMath Mode Input
` x+b/(2a)=+-sqrt((b^2)/(4a^2)-c/a) `
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Powers and indices
\[ k_{n+1} = n^2 + k_n^2 - k_{n-1} \]
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Fractions and Binomials
\[ \frac{n!}{k!(n-k)!} = \binom{n}{k} \]
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Multiplication of two numbers
\[ \begin{equation} \frac{ \begin{array}[b]{r} \left( x_1 x_2 \right)\\ \times \left( x'_1 x'_2 \right) \end{array} }{ \left( y_1y_2y_3y_4 \right) } \end{equation} \]
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Sums and integrals
\[ \sum_{i=1}^{15} t_i \]
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Automatic sizing
\[ \left(\frac{x^5}{y^8}\right) \]
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Matrices and arrays
\[ \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \]
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Controlling horizontal spacing
\[ f(n) = \left\{ \begin{array}{l l} n/2 & \quad \text{if $n$ is even}\\ -(n+1)/2 & \quad \text{if $n$ is odd}\\ \end{array} \right. \]
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The Cauchy-Schwarz Inequality
\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
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A Cross Product Formula
\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]
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A Rogers-Ramanujan Identity
\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})} \]
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