| 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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