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AiryBi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/03.06.13.0015.01









  


  








Input Form





Wronskian[s^z AiryAi[a r^z], s^z AiryBi[a r^z], z] == (a r^z s^(2 z) Log[r])/Pi








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s", "z"], RowBox[List["AiryAi", "[", RowBox[List["a", " ", SuperscriptBox["r", "z"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s", "z"], RowBox[List["AiryBi", "[", RowBox[List["a", " ", SuperscriptBox["r", "z"]]], "]"]]]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]]]], "\[Pi]"]]]]]








MathML Form







<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> s </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <msup> <mi> s </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> r </mi> <mi> z </mi> </msup> <mo> &#8290; </mo> <msup> <mi> s </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> r </mi> <mo> ) </mo> </mrow> </mrow> <mi> &#960; </mi> </mfrac> </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> s </ci> <ci> z </ci> </apply> <apply> <ci> AiryAi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> s </ci> <ci> z </ci> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> r </ci> <ci> z </ci> </apply> <apply> <power /> <ci> s </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> r </ci> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Wronskian", "[", RowBox[List[RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["AiryAi", "[", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]], "]"]]]], ",", RowBox[List[SuperscriptBox["s_", "z_"], " ", RowBox[List["AiryBi", "[", RowBox[List["a_", " ", SuperscriptBox["r_", "z_"]]], "]"]]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["a", " ", SuperscriptBox["r", "z"], " ", SuperscriptBox["s", RowBox[List["2", " ", "z"]]], " ", RowBox[List["Log", "[", "r", "]"]]]], "\[Pi]"]]]]]


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





2007-05-02