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 AiryBi

 http://functions.wolfram.com/03.06.21.0037.01

 Input Form

 Integrate[AiryBi[a z^r]^2, z] == (1/(3 r)) (2 (2/3)^(1/3) Sqrt[Pi] z MeijerG[{{1 - 1/(3 r)}, {5/6}}, {{1/3}, {0, 2/3, -(1/(3 r))}}, (2/3)^(2/3) a z^r, 1/3]) + (z MeijerG[{{1 - 1/(3 r)}, {5/6}}, {{0, 1/3, 2/3}, {-(1/(3 r))}}, (2/3)^(2/3) a z^r, 1/3])/(2 2^(2/3) 3^(1/3) Pi^(3/2) r)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", " ", RowBox[List[SuperscriptBox[RowBox[List["AiryBi", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]], "2"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["3", " ", "r"]]], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["\[Pi]"], " ", "z", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["5", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "3"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["2", "3"], ",", RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], ",", FractionBox["1", "3"]]], "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["z", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["5", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], ",", FractionBox["1", "3"]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", "r"]], ")"]]]]]]]]]]

 MathML Form

 Bi ( a z r ) 2 z 2 π z 2 3 3 3 r G 2 , 4 1 , 1 ( ( 2 3 ) 2 / 3 a z r , 1 3 1 - 1 3 r , 5 6 1 3 , 0 , 2 3 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["1", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + z 2 2 2 / 3 3 3 π 3 / 2 r G 2 , 4 3 , 1 ( ( 2 3 ) 2 / 3 a z r , 1 3 1 - 1 3 r , 5 6 0 , 1 3 , 2 3 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["3", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] z AiryBi a z r 2 2 1 2 z 2 3 1 3 3 r -1 MeijerG 1 -1 1 3 r -1 5 6 1 3 0 2 3 -1 1 3 r -1 2 3 2 3 a z r 1 3 z 2 2 2 3 3 1 3 3 2 r -1 MeijerG 1 -1 1 3 r -1 5 6 0 1 3 2 3 -1 1 3 r -1 2 3 2 3 a z r 1 3 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["AiryBi", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]], "2"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["1", "/", "3"]]], " ", SqrtBox["\[Pi]"], " ", "z", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["5", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "3"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["2", "3"], ",", RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], ",", FractionBox["1", "3"]]], "]"]]]], RowBox[List["3", " ", "r"]]], "+", FractionBox[RowBox[List["z", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["5", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "a", " ", SuperscriptBox["z", "r"]]], ",", FractionBox["1", "3"]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", "r"]]]]]]]]]

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

 2001-10-29