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http://functions.wolfram.com/03.02.13.0030.01
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Wronskian[z^p BesselI[\[Nu], m z^q], z^p BesselI[-\[Nu], m z^q], z] ==
-((2 q z^(2 p - 1) Sin[Pi \[Nu]])/Pi)
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z", "p"], RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]], ",", " ", RowBox[List[SuperscriptBox["z", "p"], RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["m", " ", SuperscriptBox["z", "q"]]]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "q", " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "p"]], "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "\[Pi]"]]]]]]]
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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> <mrow> <msup> <mi> z </mi> <mi> p </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> q </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> z </mi> <mi> p </mi> </msup> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> q </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mi> π </mi> </mfrac> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> p </ci> </apply> <apply> <ci> BesselI </ci> <ci> ν </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> p </ci> </apply> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> z </ci> <ci> q </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> q </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["z_", "p_"], " ", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", RowBox[List["m_", " ", SuperscriptBox["z_", "q_"]]]]], "]"]]]], ",", RowBox[List[SuperscriptBox["z_", "p_"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", RowBox[List["m_", " ", SuperscriptBox["z_", "q_"]]]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "q", " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "p"]], "-", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "\[Pi]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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