AiryAiPrime[z] == (1/3) z (BesselI[2/3, (2 z^(3/2))/3] - BesselI[-(2/3), (2 z^(3/2))/3]) /; Re[z] >= 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryAiPrime", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "3"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List[FractionBox["2", "3"], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]], "-", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> Ai </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </msub> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msub> <mi> I </mi> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> AiryAiPrime </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <ci> z </ci> <apply> <plus /> <apply> <ci> BesselI </ci> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> BesselI </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <geq /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryAiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "3"], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List[FractionBox["2", "3"], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]], "-", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]

2001-10-29