MathWiki_20_query.json

{
   "queries" : [
    "-0.026838601\\ldots",
    "\\mathfrak{P}",
    "N = \\left\\lfloor 0.5 - \\log_{2} \\left(\\frac{\\text{Frequency of this item}}{\\text{Frequency of most common item}}\\right) \\right\\rfloor",
    "\\nabla \\times \\mathbf{B} = \\mu_{0} \\mathbf{J} +\\underbrace{\\mu_{0}\\epsilon_{0} \\frac{\\partial}{\\partial t}\\mathbf{E}}_{\\text{Maxwell's term}}",
    "1 + \\cfrac{1}{2 + \\cfrac{1}{5 + \\cfrac{1}{5 + \\cfrac{1}{4 + \\ddots}}}}",
    "^{238}_{92}\\mathrm{U} + ^{64}_{28}\\mathrm{Ni} \\;\\rightarrow\\;^{302}_{120}\\mathrm{Ubn}^{*} \\;\\rightarrow\\; \\textit{fission only}",
    "0 \\rightarrow G^\\wedge \\xrightarrow{\\pi^\\wedge} X^\\wedge \\xrightarrow{i^\\wedge} H^\\wedge \\rightarrow 0",
    "w = \\begin{cases} w^* & \\text{if } w^* > \\frac{1}{2}, \\\\ \\frac{1}{2} & \\text{if } w^* \\le \\frac{1}{2}. \\end{cases}",
    "\\begin{bmatrix} V_1 \\\\ I_2 \\end{bmatrix} = \\begin{bmatrix} h_{11} & h_{12} \\\\ h_{21} & h_{22} \\end{bmatrix} \\begin{bmatrix} I_1 \\\\ V_2 \\end{bmatrix}",
    "L(\\lambda, \\alpha, s) = \\sum_{n=0}^{\\infty} \\frac{\\exp(2\\pi i\\lambda n)}{(n+\\alpha)^s}.",
    "ax^{2} + bx + c = 0",
    "O(mn \\log m)",
    "A \\oplus B = (A^c \\ominus B^s)^c",
    "\\cos \\alpha = -\\cos \\beta \\cos \\gamma + \\sin \\beta \\sin \\gamma \\cosh \\frac{a}{k},",
    "\\forall x, y \\in A \\ [x \\neq y \\rightarrow \\neg \\exists z \\in X \\ [z \\leq x \\wedge z \\leq y]]",
    "\\tau_{\\text{rms}} = \\sqrt{\\frac{\\int_{0}^{\\infty} (\\tau - \\bar{\\tau})^{2} A_c(\\tau)\\, d\\tau}{\\int_{0}^{\\infty} A_c(\\tau)\\, d\\tau}}",
    "x - 1 - \\frac{1}{2} - \\frac{1}{4} - \\frac{1}{5} - \\frac{1}{6} - \\frac{1}{9} - \\cdots = 1",
    "P(x_{i}) = \\frac{N!}{n_{x}!(N-n_{x})!} p^{n_{x}}_{x} (1-p_{x})^{N-n_{x}}",
    "H_{ij} = \\begin{bmatrix} \\frac{\\partial^{2}V_{ij}}{\\partial x_{i}\\partial x_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial x_{i}\\partial y_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial x_{i}\\partial z_{j}} \\\\ \\frac{\\partial^{2}V_{ij}}{\\partial y_{i}\\partial x_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial y_{i}\\partial y_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial y_{i}\\partial z_{j}} \\\\ \\frac{\\partial^{2}V_{ij}}{\\partial z_{i}\\partial x_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial z_{i}\\partial y_{j}} & \\frac{\\partial^{2}V_{ij}}{\\partial z_{i}\\partial z_{j}} \\end{bmatrix}",
    "r_{xy} = \\frac{\\sum_{i=1}^{n} (x_i - \\bar{x})(y_i - \\bar{y})}{(n-1) s_x s_y} = \\frac{\\sum_{i=1}^{n} (x_i - \\bar{x})(y_i - \\bar{y})}{\\sqrt{\\sum_{i=1}^{n} (x_i - \\bar{x})^2 \\sum_{i=1}^{n} (y_i - \\bar{y})^2}},"
   ]
}