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http://functions.wolfram.com/03.07.13.0005.01
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Wronskian[AiryAiPrime[z], AiryAiPrime[z/E^((2 Pi I)/3)], z] ==
z/(2 Pi)/E^((Pi I)/6)
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Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], ",", RowBox[List["AiryAiPrime", "[", RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "3"]]]]]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["z", RowBox[List["2", "\[Pi]"]]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "6"]]]]]]]]]]
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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> Ai </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msup> <mi> Ai </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 3 </mn> </mfrac> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 6 </mn> </mfrac> </mrow> <mtext> </mtext> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> W </ci> <ci> z </ci> </apply> <apply> <ci> AiryAiPrime </ci> <ci> z </ci> </apply> <apply> <ci> AiryAiPrime </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </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["AiryAiPrime", "[", "z_", "]"]], ",", RowBox[List["AiryAiPrime", "[", RowBox[List["z_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "6"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]], RowBox[List["2", " ", "\[Pi]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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