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AiryBiPrime




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.08.21.0081.01









  


  








Input Form





Integrate[z^2 AiryBi[a z] AiryBiPrime[a z], z] == (1/(6 a^3)) (a^2 z^2 AiryBi[a z]^2 - 2 AiryBi[a z] AiryBiPrime[a z] + 2 a z AiryBiPrime[a z]^2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["6", " ", SuperscriptBox["a", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]], "-", RowBox[List["2", " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", "a", " ", "z", " ", SuperscriptBox[RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> AiryBi </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> <apply> <power /> <apply> <ci> AiryBiPrime </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["AiryBi", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]], "-", RowBox[List["2", " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", "a", " ", "z", " ", SuperscriptBox[RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], "2"]]]]], RowBox[List["6", " ", SuperscriptBox["a", "3"]]]]]]]]


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





2001-10-29