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AiryAiPrime






Mathematica Notation

Traditional Notation









Bessel-Type Functions > AiryAiPrime[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/03.07.21.0082.01









  


  










Input Form





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










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["AiryAiPrime", "[", 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[RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", "a", " ", "z", " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["AiryAi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]










MathML Form







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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["AiryAiPrime", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["2", " ", "a", " ", "z", " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["AiryAi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]], RowBox[List["6", " ", SuperscriptBox["a", "3"]]]]]]]]










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





2001-10-29