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http://functions.wolfram.com/10.07.13.0012.01
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Wronskian[z^s, z^s Log[a z^r], z^s PolyLog[2, a z^r], z] ==
(a r^3 z^(-3 + r + 3 s))/(1 - a z^r)
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[SuperscriptBox["z", "s"], ",", RowBox[List[SuperscriptBox["z", "s"], RowBox[List["Log", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z", "s"], RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["a", " ", SuperscriptBox["r", "3"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "+", "r", "+", RowBox[List["3", " ", "s"]]]]]]], RowBox[List["1", "-", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> W </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mi> s </mi> </msup> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> s </mi> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> s </mi> </msup> <mo> ⁢ </mo> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> r </mi> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> r </mi> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> s </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <ci> s </ci> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> s </ci> </apply> <apply> <ln /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> s </ci> </apply> <apply> <ci> Subscript </ci> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> r </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> s </ci> </apply> <cn type='integer'> -3 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[SuperscriptBox["z_", "s_"], ",", RowBox[List[SuperscriptBox["z_", "s_"], " ", RowBox[List["Log", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "s_"], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["a", " ", SuperscriptBox["r", "3"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "3"]], "+", "r", "+", RowBox[List["3", " ", "s"]]]]]]], RowBox[List["1", "-", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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