html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 AiryAiPrime

 http://functions.wolfram.com/03.07.21.0014.01

 Input Form

 Integrate[(Sqrt[z] AiryAiPrime[a z])/E^((2/3) (a z)^(3/2)), z] == (1/(21 a^2 Sqrt[z] Gamma[1/3])) ((6 a^2 z^2 AiryAiPrime[a z] Gamma[1/3] + 2 Sqrt[a z] (-2 3^(2/3) E^((2/3) (a z)^(3/2)) - (a^3 z^3 BesselI[-(5/3), (2/3) a^(3/2) z^(3/2)] Gamma[1/3])/ (a^(3/2) z^(3/2))^(1/3) + a^2 z^2 (a^(3/2) z^(3/2))^(1/3) BesselI[5/3, (2/3) a^(3/2) z^(3/2)] Gamma[1/3]))/E^((2/3) (a z)^(3/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SqrtBox["z"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["21", " ", SuperscriptBox["a", "2"], " ", SqrtBox["z"], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["2", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["5", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z - 2 3 ( a z ) 3 / 2 Ai ( a z ) z 1 21 a 2 z Γ ( 1 3 ) ( 1 3 ( - 2 ) ( a z ) 3 / 2 ( 6 a 2 Ai ( a z ) Γ ( 1 3 ) z 2 + 2 a z ( a 2 z 2 I 5 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 1 3 ) a 3 / 2 z 3 / 2 3 - 2 3 2 / 3 2 3 ( a z ) 3 / 2 - a 3 z 3 Γ ( 1 3 ) a 3 / 2 z 3 / 2 3 I - 5 3 ( 2 3 a 3 / 2 z 3 / 2 ) ) ) ) z z 1 2 -1 2 3 a z 3 2 AiryAiPrime a z 1 21 a 2 z 1 2 Gamma 1 3 -1 1 3 -2 a z 3 2 6 a 2 AiryAiPrime a z Gamma 1 3 z 2 2 a z 1 2 a 2 z 2 BesselI 5 3 2 3 a 3 2 z 3 2 Gamma 1 3 a 3 2 z 3 2 1 3 -1 2 3 2 3 2 3 a z 3 2 -1 a 3 z 3 Gamma 1 3 a 3 2 z 3 2 1 3 -1 BesselI -1 5 3 2 3 a 3 2 z 3 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SqrtBox["z_"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", " ", "z_"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["AiryAiPrime", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "2"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["AiryAiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["5", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["5", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["21", " ", SuperscriptBox["a", "2"], " ", SqrtBox["z"], " ", RowBox[List["Gamma", "[", FractionBox["1", "3"], "]"]]]]]]]]]

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

 2001-10-29