data/190.json
{
"definitions" : {
"\\theta_{\\infty}" : [ {
"Q188248" : "constant"
} ],
"z" : [ {
"Q11567" : "complex number"
} ],
"v_k" : [ {
"Q11348" : "function"
} ],
"v_k'" : [ {
"Q29175" : "derivative"
} ],
"u_k" : [ {
"Q11348" : "function"
} ]
},
"constraints" : [ ],
"math_inputtex" : "\\[zv_{1}^{\\prime}=2u_{0}-2u_{1}v_{1}^{2}-\\theta_{\\infty}v_{1}.\\]",
"math_inputtex_semantic" : "\\w{Q11567}{z} \\w{Q11348}{v}_1' = 2 \\w{Q11348}{u}_0 - 2u_1 v_1^2 - \\w{Q188248}{\\theta_{\\infty}} v_1",
"correct_tex" : "zv_{1}^{\\prime}=2u_{0}-2u_{1}v_{1}^{2}-\\theta_{\\infty}v_{1}",
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id=\"p1.1.m1.1.21.2.1.1\" xref=\"p1.1.m1.1.21.2.1.1.cmml\"></mo>\n <msub id=\"p1.1.m1.1.21.2.1.2\" xref=\"p1.1.m1.1.21.2.1.2.cmml\">\n <mi id=\"p1.1.m1.1.7\" xref=\"p1.1.m1.1.7.cmml\">u</mi>\n <mn id=\"p1.1.m1.1.8.1\" xref=\"p1.1.m1.1.8.1.cmml\">0</mn>\n </msub>\n </mrow>\n <mo id=\"p1.1.m1.1.9\" xref=\"p1.1.m1.1.9.cmml\">-</mo>\n <mrow id=\"p1.1.m1.1.21.2.2\" xref=\"p1.1.m1.1.21.2.2.cmml\">\n <mn id=\"p1.1.m1.1.10\" xref=\"p1.1.m1.1.10.cmml\">2</mn>\n <mo id=\"p1.1.m1.1.21.2.2.1\" xref=\"p1.1.m1.1.21.2.2.1.cmml\"></mo>\n <msub id=\"p1.1.m1.1.21.2.2.2\" xref=\"p1.1.m1.1.21.2.2.2.cmml\">\n <mi id=\"p1.1.m1.1.11\" xref=\"p1.1.m1.1.11.cmml\">u</mi>\n <mn id=\"p1.1.m1.1.12.1\" xref=\"p1.1.m1.1.12.1.cmml\">1</mn>\n </msub>\n <mo id=\"p1.1.m1.1.21.2.2.1a\" xref=\"p1.1.m1.1.21.2.2.1.cmml\"></mo>\n <msubsup id=\"p1.1.m1.1.21.2.2.3\" xref=\"p1.1.m1.1.21.2.2.3.cmml\">\n <mi id=\"p1.1.m1.1.13\" xref=\"p1.1.m1.1.13.cmml\">v</mi>\n <mn id=\"p1.1.m1.1.14.1\" xref=\"p1.1.m1.1.14.1.cmml\">1</mn>\n <mn id=\"p1.1.m1.1.15.1\" xref=\"p1.1.m1.1.15.1.cmml\">2</mn>\n </msubsup>\n </mrow>\n <mo id=\"p1.1.m1.1.9a\" xref=\"p1.1.m1.1.9.cmml\">-</mo>\n <mrow id=\"p1.1.m1.1.21.2.3\" xref=\"p1.1.m1.1.21.2.3.cmml\">\n <msub id=\"p1.1.m1.1.21.2.3.2\" xref=\"p1.1.m1.1.21.2.3.2.cmml\">\n <mi id=\"p1.1.m1.1.17\" xref=\"p1.1.m1.1.17.cmml\">θ</mi>\n <mi mathvariant=\"normal\" id=\"p1.1.m1.1.18.1\" xref=\"p1.1.m1.1.18.1.cmml\">∞</mi>\n </msub>\n <mo id=\"p1.1.m1.1.21.2.3.1\" xref=\"p1.1.m1.1.21.2.3.1.cmml\"></mo>\n <msub id=\"p1.1.m1.1.21.2.3.3\" xref=\"p1.1.m1.1.21.2.3.3.cmml\">\n <mi id=\"p1.1.m1.1.19\" xref=\"p1.1.m1.1.19.cmml\">v</mi>\n <mn id=\"p1.1.m1.1.20.1\" xref=\"p1.1.m1.1.20.1.cmml\">1</mn>\n </msub>\n </mrow>\n </mrow>\n </mrow>\n <annotation-xml encoding=\"MathML-Content\" id=\"p1.1.m1.1b\">\n <apply id=\"p1.1.m1.1.21.cmml\" xref=\"p1.1.m1.1.21\">\n <eq id=\"p1.1.m1.1.5.cmml\" xref=\"p1.1.m1.1.5\"/>\n <apply id=\"p1.1.m1.1.21.1.cmml\" xref=\"p1.1.m1.1.21.1\">\n <times 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xref=\"p1.1.m1.1.6\">2</cn>\n <apply id=\"p1.1.m1.1.21.2.1.2.cmml\" xref=\"p1.1.m1.1.21.2.1.2\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.1.2.1.cmml\" xref=\"p1.1.m1.1.21.2.1.2\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.7.cmml\" xref=\"p1.1.m1.1.7\">Q11348</csymbol>\n <cn type=\"integer\" id=\"p1.1.m1.1.8.1.cmml\" xref=\"p1.1.m1.1.8.1\">0</cn>\n </apply>\n </apply>\n <apply id=\"p1.1.m1.1.21.2.2.cmml\" xref=\"p1.1.m1.1.21.2.2\">\n <times id=\"p1.1.m1.1.21.2.2.1.cmml\" xref=\"p1.1.m1.1.21.2.2.1\"/>\n <cn type=\"integer\" id=\"p1.1.m1.1.10.cmml\" xref=\"p1.1.m1.1.10\">2</cn>\n <apply id=\"p1.1.m1.1.21.2.2.2.cmml\" xref=\"p1.1.m1.1.21.2.2.2\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.2.2.1.cmml\" xref=\"p1.1.m1.1.21.2.2.2\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.11.cmml\" xref=\"p1.1.m1.1.11\">Q11348</csymbol>\n <cn type=\"integer\" id=\"p1.1.m1.1.12.1.cmml\" xref=\"p1.1.m1.1.12.1\">1</cn>\n </apply>\n <apply 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id=\"p1.1.m1.1.18.1.cmml\" xref=\"p1.1.m1.1.18.1\"/>\n </apply>\n <apply id=\"p1.1.m1.1.21.2.3.3.cmml\" xref=\"p1.1.m1.1.21.2.3.3\">\n <csymbol cd=\"ambiguous\" id=\"p1.1.m1.1.21.2.3.3.1.cmml\" xref=\"p1.1.m1.1.21.2.3.3\">subscript</csymbol>\n <csymbol cd=\"latexml\" id=\"p1.1.m1.1.19.cmml\" xref=\"p1.1.m1.1.19\">Q11348</csymbol>\n <cn type=\"integer\" id=\"p1.1.m1.1.20.1.cmml\" xref=\"p1.1.m1.1.20.1\">1</cn>\n </apply>\n </apply>\n </apply>\n </apply>\n </annotation-xml>\n <annotation encoding=\"application/x-tex\" id=\"p1.1.m1.1c\">zv_{1}^{\\prime}=2u_{0}-2u_{1}v_{1}^{2}-\\theta_{\\infty}v_{1}</annotation>\n </semantics>\n</math>",
"uri" : "http://dlmf.nist.gov/32.4#E13",
"title" : "DLMF:_32.4_Isomonodromy_Problems",
"type" : "equation"
}