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AiryBi




Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryBi[z] > Integration > Definite integration > Multiple integration





http://functions.wolfram.com/03.06.21.0085.01









  


  








Input Form





Integrate[AiryBi[t], {x, 0, x}, {t, 0, x}] == x Integrate[AiryBi[t], {t, 0, x}] - AiryBiPrime[x] + AiryBiPrime[0]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x"], RowBox[List[RowBox[List["AiryBi", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]], RowBox[List["\[DifferentialD]", "x"]]]]]]]], "\[Equal]", RowBox[List[RowBox[List["x", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x"], RowBox[List[RowBox[List["AiryBi", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "-", RowBox[List["AiryBiPrime", "[", "x", "]"]], "+", RowBox[List["AiryBiPrime", "[", "0", "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> x </mi> </msubsup> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> x </mi> </msubsup> <mrow> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> x </mi> </mrow> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mi> Bi </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> x </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mo> &#8747; </mo> <mn> 0 </mn> <mi> x </mi> </msubsup> <mrow> <mrow> <mi> Bi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> x </ci> </uplimit> <apply> <int /> <bvar> <ci> x </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> x </ci> </uplimit> <apply> <ci> AiryBi </ci> <ci> t </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> AiryBiPrime </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> AiryBiPrime </ci> <ci> x </ci> </apply> </apply> <apply> <times /> <ci> x </ci> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> x </ci> </uplimit> <apply> <ci> AiryBi </ci> <ci> t </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x_"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x_"], RowBox[List[RowBox[List["AiryBi", "[", "t_", "]"]], RowBox[List["\[DifferentialD]", "t_"]], RowBox[List["\[DifferentialD]", "x_"]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "x"], RowBox[List[RowBox[List["AiryBi", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "-", RowBox[List["AiryBiPrime", "[", "x", "]"]], "+", RowBox[List["AiryBiPrime", "[", "0", "]"]]]]]]]]


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





2001-10-29