Poject:GoldData

Result table

#	Formula	Title	Evaluation data
1	\begin{align}J_{-(m+\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\frac{1}{2}}(x), \\Y_{-(m+\frac{1}{2})}(x) &= (-1)^m J_{m+\frac{1}{2}}(x).\end{align}	Bessel function	Full data: { "id": 1, "pid": 51, "eid": "math.51.18", "title": "Bessel function", "formulae": [ { "id": "FORMULA_0f521573a47e7fd187dafed615b0ecce", "formula": "\\begin{align}J_{-(m+\\frac{1}{2})}(x) &= (-1)^{m+1} Y_{m+\\frac{1}{2}}(x), \\\\Y_{-(m+\\frac{1}{2})}(x) &= (-1)^m J_{m+\\frac{1}{2}}(x).\\end{align}", "semanticFormula": "\\begin{align}\\BesselJ{- (m + \\frac{1}{2})}@{x} &= (- 1)^{m+1} \\BesselY{m+\\frac{1}{2}}@{x} , \\\\ \\BesselY{- (m + \\frac{1}{2})}@{x} &= (-1)^m \\BesselJ{m+\\frac{1}{2}}@{x} .\\end{align}", "confidence": 0.8803349492974287, "translations": { "Mathematica": { "translation": "BesselJ[- (m +Divide[1,2]), x] == (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]\nBesselY[- (m +Divide[1,2]), x] == (- 1)^(m)* BesselJ[m +Divide[1,2], x]", "translationInformation": { "subEquations": [ "BesselJ[- (m +Divide[1,2]), x] = (- 1)^(m + 1)* BesselY[m +Divide[1,2], x]", "BesselY[- (m +Divide[1,2]), x] = (- 1)^(m)* BesselJ[m +Divide[1,2], x]" ], "freeVariables": [ "m", "x" ], "constraints": [], "tokenTranslations": { "\\pgcd": "Greatest common divisor; Example: \\pgcd{m,n}\nWill be translated to: GCD[$0]\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/27.1#p2.t1.r3\nMathematica: https:\/\/reference.wolfram.com\/language\/ref\/GCD.html", "\\BesselY": "Bessel function second kind; Example: \\BesselY{v}@{z}\nWill be translated to: BesselY[$0, $1]\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/10.2#E3\nMathematica: https:\/\/", "\\BesselJ": "Bessel function first kind; Example: \\BesselJ{v}@{z}\nWill be translated to: BesselJ[$0, $1]\nBranch Cuts: if v \\notin \\Integers: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/10.2#E2\nMathematica: https:\/\/reference.wolfram.com\/language\/ref\/BesselJ.html" } } }, "Maple": { "translation": "BesselJ(- (m +(1)\/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)\/(2), x); BesselY(- (m +(1)\/(2)), x) = (- 1)^(m)* BesselJ(m +(1)\/(2), x)", "translationInformation": { "subEquations": [ "BesselJ(- (m +(1)\/(2)), x) = (- 1)^(m + 1)* BesselY(m +(1)\/(2), x)", "BesselY(- (m +(1)\/(2)), x) = (- 1)^(m)* BesselJ(m +(1)\/(2), x)" ], "freeVariables": [ "m", "x" ], "constraints": [], "tokenTranslations": { "\\pgcd": "Greatest common divisor; Example: \\pgcd{m,n}\nWill be translated to: gcd($0)\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/27.1#p2.t1.r3\nMaple: https:\/\/www.maplesoft.com\/support\/help\/Maple\/view.aspx?path=gcd", "\\BesselY": "Bessel function second kind; Example: \\BesselY{v}@{z}\nWill be translated to: BesselY($0, $1)\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/10.2#E3\nMaple: https:\/\/www.maplesoft.com\/support\/help\/maple\/view.aspx?path=Bessel", "\\BesselJ": "Bessel function first kind; Example: \\BesselJ{v}@{z}\nWill be translated to: BesselJ($0, $1)\nBranch Cuts: if v \\notin \\Integers: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http:\/\/dlmf.nist.gov\/10.2#E2\nMaple: https:\/\/www.maplesoft.com\/support\/help\/maple\/view.aspx?path=Bessel" } } } }, "positions": [ { "section": 8, "sentence": 8, "word": 32 } ], "includes": [ "Y_{\\alpha}", "J_{-\\alpha}(x)", "J", "J_{\\alpha}(x)", "Y_{n}", "J_{n}(x)", "m", "Y_{\\alpha}(x)", "J_{\\alpha}", "x", "(-1)^{m}", "J_{n}", "J_{\\alpha}(z)", "J_{\\alpha}(k)", "Y", "J_{n + m}(x)" ], "isPartOf": [], "definiens": [ { "definition": "Bessel function first kind", "score": 2 }, { "definition": "Bessel function second kind", "score": 2 }, { "definition": "above relation", "score": 0 }, { "definition": "spherical Bessel", "score": 1 }, { "definition": "integer", "score": 1 }, { "definition": "nonnegative integer", "score": 1 }, { "definition": "relationship", "score": 0 }, { "definition": "function", "score": 1 }, { "definition": "recurrence relation", "score": 1 }, { "definition": "Bessel", "score": 1 }, { "definition": "large number of other known integral", "score": 0 }, { "definition": "positive zero", "score": 0 }, { "definition": "entire function of genus", "score": 0 }, { "definition": "identity", "score": 0 }, { "definition": "orthogonality relation", "score": 0 }, { "definition": "Bessel function", "score": 2 }, { "definition": "term", "score": 0 }, { "definition": "real zero", "score": 0 }, { "definition": "similar relation", "score": 0 }, { "definition": "Hankel", "score": 1 }, { "definition": "Bessel function of the second kind", "score": 2 }, { "definition": "limit", "score": 0 }, { "definition": "ordinary Bessel function", "score": 1 }, { "definition": "case", "score": 0 }, { "definition": "negative integer", "score": 0 }, { "definition": "integral formula", "score": 0 }, { "definition": "small argument", "score": 0 }, { "definition": "average", "score": 0 }, { "definition": "Bessel function of the first kind", "score": 2 }, { "definition": "reference", "score": 0 }, { "definition": "series expansion", "score": 0 }, { "definition": "spherical Bessel function", "score": 1 }, { "definition": "Abel 's identity", "score": 0 }, { "definition": "important property of Bessel 's equation", "score": 1 }, { "definition": "particular Bessel", "score": 1 }, { "definition": "solution of Bessel 's equation", "score": 0 }, { "definition": "Wronskian of the solution", "score": 0 }, { "definition": "series", "score": 0 }, { "definition": "closure equation", "score": 0 } ] } ] } |-