data/261.json
{
"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"
}