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AiryBi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Integration > Indefinite integration > Involving direct function and Bessel-type functions > Involving other Airy functions > Involving Ai > Linear arguments





http://functions.wolfram.com/03.06.21.0088.01









  


  








Input Form





Integrate[(1/AiryAi[z]^2) f[AiryBi[z]/AiryAi[z]], z] == Pi F[AiryBi[z]/AiryAi[z]] /; Derivative[1][F][\[Zeta]] == f[\[Zeta]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["AiryAi", "[", "z", "]"]], "2"], " "]]], RowBox[List["f", "[", FractionBox[RowBox[List["AiryBi", "[", "z", "]"]], RowBox[List["AiryAi", "[", "z", "]"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["\[Pi]", " ", RowBox[List["F", "[", FractionBox[RowBox[List["AiryBi", "[", "z", "]"]], RowBox[List["AiryAi", "[", "z", "]"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["F", "'"]], "[", "\[Zeta]", "]"]], "\[Equal]", RowBox[List["f", "[", "\[Zeta]", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> &#8290; </mo> <mrow> <mi> f </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> F </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> Ai </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msup> <mi> F </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> &#950; </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> f </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#950; </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> f </ci> <apply> <times /> <apply> <ci> AiryBi </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <ci> EllipticF </ci> <apply> <times /> <apply> <ci> AiryBi </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> &#950; </ci> </bvar> <apply> <ci> F </ci> <ci> &#950; </ci> </apply> </apply> <apply> <ci> f </ci> <ci> &#950; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["f", "[", FractionBox[RowBox[List["AiryBi", "[", "z_", "]"]], RowBox[List["AiryAi", "[", "z_", "]"]]], "]"]], SuperscriptBox[RowBox[List["AiryAi", "[", "z_", "]"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["F", "[", FractionBox[RowBox[List["AiryBi", "[", "z", "]"]], RowBox[List["AiryAi", "[", "z", "]"]]], "]"]]]], "/;", RowBox[List[RowBox[List[SuperscriptBox["F", "\[Prime]", Rule[MultilineFunction, None]], "[", "\[Zeta]", "]"]], "\[Equal]", RowBox[List["f", "[", "\[Zeta]", "]"]]]]]]]]]]


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





2002-12-18