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AiryBiPrime




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBiPrime[z] > Representations through more general functions > Through other functions > Involving Bessel functions





http://functions.wolfram.com/03.08.26.0020.01









  


  








Input Form





AiryBiPrime[z] == (1/Sqrt[3]) ((z^2 BesselI[2/3, (2 z^(3/2))/3])/ (z^(3/2))^(2/3) + (z^(3/2))^(2/3) BesselI[-(2/3), (2 z^(3/2))/3])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["AiryBiPrime", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["3"]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], SuperscriptBox[RowBox[List["(", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], ")"]], RowBox[List["-", FractionBox["2", "3"]]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["2", "3"], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mn> 3 </mn> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mo> &#8290; </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> <mtext> </mtext> <mo> + </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <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> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> AiryBiPrime </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <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> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBiPrime", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], ")"]], RowBox[List["-", FractionBox["2", "3"]]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["2", "3"], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]]]], SqrtBox["3"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29