mathmlben/data/261.json

Visualization for goldstandard

{
  "definitions": {
    "k": [
      "number of annual payments",
      {
        "Q28920044": "positive integer",
        "Q2303886": "index number"
      }
    ],
    "p": [
      "payment",
      {
        "Q3176558": "positive real number"
      }
    ],
    "q": [
      "payment increase per period",
      {
        "Q12916": "real number"
      }
    ],
    "({\\ddot{s}}_{a})_{\\overline{k}|j}^{(p,q)}": [
      "accumulated value of an annuity-due with payments varying in arithmetic progression",
      {
        "Q18729403": "non-negative real number"
      }
    ],
    "C_{k}": [
      "final value of an annuity-due with payments varying in arithmetic progression",
      {
        "Q18729403": "non-negative real number"
      }
    ],
    "E": [
      {
        "Q200125": "expected value",
        "Q11348": "function"
      }
    ]
  },
  "constraints": [],
  "math_inputtex": "{\\mu}_{k}=E(C_{k})=({\\ddot{s}}_{a})_{\\overline{k}|j}^{(p,q)}.",
  "math_inputtex_semantic": "{\\mu}_{\\w{Q1738991}{k}} = \\wf{Q200125}{E}(\\w{Q18729403}{C}_{k})",
  "correct_tex": "{\\mu}_{k}=E(C_{k})=({\\ddot{s}}_{a})_{\\overline{k}|j}^{(p,q)}",
  "correct_mml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"\n      xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n      alttext=\"{\\mu}_{k}=E(C_{k})\"\n      class=\"ltx_Math\"\n      display=\"inline\"\n      id=\"p1.1.m1.1\">\n  <semantics id=\"p1.1.m1.1a\">\n      <mrow id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">\n         <msub id=\"p1.1.m1.1.9.1\" xref=\"p1.1.m1.1.9.1.cmml\">\n            <mi id=\"p1.1.m1.1.1\" xref=\"p1.1.m1.1.1.cmml\">μ</mi>\n            <mi id=\"p1.1.m1.1.2.1\" xref=\"p1.1.m1.1.2.1.cmml\">k</mi>\n         </msub>\n         <mo id=\"p1.1.m1.1.3\" xref=\"p1.1.m1.1.3.cmml\">=</mo>\n         <mrow id=\"p1.1.m1.1.9.2.2\" xref=\"p1.1.m1.1.9.2.1.cmml\">\n            <mi id=\"p1.1.m1.1.4\" xref=\"p1.1.m1.1.4.cmml\">E</mi>\n            <mo id=\"p1.1.m1.1.9.2.2a\" xref=\"p1.1.m1.1.9.2.1.cmml\">⁡</mo>\n            <mrow id=\"p1.1.m1.1.9.2.2.2\" xref=\"p1.1.m1.1.9.2.1.cmml\">\n               <mo id=\"p1.1.m1.1.5\" stretchy=\"false\" xref=\"p1.1.m1.1.9.2.1.cmml\">(</mo>\n               <msub id=\"p1.1.m1.1.9.2.2.1\" xref=\"p1.1.m1.1.9.2.2.1.cmml\">\n                  <mi id=\"p1.1.m1.1.6\" xref=\"p1.1.m1.1.6.cmml\">C</mi>\n                  <mi id=\"p1.1.m1.1.7.1\" xref=\"p1.1.m1.1.7.1.cmml\">k</mi>\n               </msub>\n               <mo id=\"p1.1.m1.1.8\" stretchy=\"false\" xref=\"p1.1.m1.1.9.2.1.cmml\">)</mo>\n            </mrow>\n         </mrow>\n      </mrow>\n      <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n         <apply id=\"p1.1.m1.1.9.cmml\" xref=\"p1.1.m1.1.9\">\n            <eq id=\"p1.1.m1.1.3.cmml\" xref=\"p1.1.m1.1.3\"/>\n            <apply id=\"p1.1.m1.1.9.1.cmml\" xref=\"p1.1.m1.1.9.1\">\n               <ci id=\"p1.1.m1.1.1.cmml\" xref=\"p1.1.m1.1.1\">𝜇</ci>\n               <ci id=\"p1.1.m1.1.2.1.cmml\" xref=\"p1.1.m1.1.2.1\">𝑘</ci>\n            </apply>\n            <apply id=\"p1.1.m1.1.9.2.1.cmml\" xref=\"p1.1.m1.1.9.2.2\">\n               <csymbol cd=\"wikidata\" id=\"p1.1.m1.1.4.cmml\" xref=\"p1.1.m1.1.4\">Q200125</csymbol>\n               <apply id=\"p1.1.m1.1.9.2.2.1.cmml\" xref=\"p1.1.m1.1.9.2.2.1\">\n                  <ci id=\"p1.1.m1.1.6.cmml\" xref=\"p1.1.m1.1.6\">𝐶</ci>\n                  <ci id=\"p1.1.m1.1.7.1.cmml\" xref=\"p1.1.m1.1.7.1\">𝑘</ci>\n               </apply>\n            </apply>\n         </apply>\n      </annotation-xml>\n      <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">{\\mu}_{k}=E(C_{k})</annotation>\n  </semantics>\n</math>\n",
  "uri": "https://arxiv.org/abs/math/0112298",
  "title": "Arithmetic Progression Context 2",
  "comment": "disregarded first random formula here because it was simply i_k. {\\mu}_{k} is a variable?",
  "type": "equation",
  "ntcir12-type": "3",
  "formula": "1_36.8",
  "page": "6",
  "ntcir12-relevance": "4"
}