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http://functions.wolfram.com/07.41.03.0010.01
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ParabolicCylinderD[-(1/2), z] ==
(Sqrt[Pi]/2) ((z^2)^(1/4) BesselI[-(1/4), z^2/4] -
(z/(z^2)^(1/4)) BesselI[1/4, z^2/4])
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Cell[BoxData[RowBox[List[RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox["\[Pi]"], "2"], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["z", " "]], SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]]], RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]]]], ")"]]]]]]]]
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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> <semantics> <mi> D </mi> <annotation encoding='Mathematica'> TagBox["D", ParabolicCylinderD] </annotation> </semantics> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <msqrt> <mi> π </mi> </msqrt> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mroot> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mi> z </mi> <mtext> </mtext> </mrow> <mroot> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mroot> </mfrac> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </msub> <mo> ( </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ParabolicCylinderD </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ParabolicCylinderD", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], "-", FractionBox[RowBox[List["z", " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "2"], ")"]], RowBox[List["1", "/", "4"]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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