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; }

 AiryBiPrime

 http://functions.wolfram.com/03.08.21.0059.01

 Input Form

 Integrate[BesselK[2, (2/3) (a z^r)^(3/2)] AiryBiPrime[a z^r], z] == (-(1/(8 2^(2/3) 3^(5/6) Pi^(3/2) r))) (z (MeijerG[{{1/3, 5/6, 1 - 1/(3 r)}, {-(13/6)}}, {{-1, -(1/3), 1, 5/3}, {-(13/6), -(1/(3 r))}}, (-(2/3)^(2/3)) a z^r, 1/3] + 2 MeijerG[{{1/3, 5/6, 1 - 1/(3 r)}, {-(1/6)}}, {{-1, -(1/3), 1, 5/3}, {-(1/6), -(1/(3 r))}}, (-(2/3)^(2/3)) a z^r, 1/3] + 4 Pi (3 Log[(-a) z^r] - 2 Log[(a z^r)^(3/2)]) MeijerG[{{1/3, 5/6, 1 - 1/(3 r)}, {4/3}}, {{1, 5/3}, {-1, -(1/3), 4/3, -(1/(3 r))}}, (-(2/3)^(2/3)) a z^r, 1/3] + MeijerG[{{1/3, 5/6, 1 - 1/(3 r)}, {11/6}}, {{-1, -(1/3), 1, 5/3}, {11/6, -(1/(3 r))}}, (-(2/3)^(2/3)) a z^r, 1/3] + 4 Pi^2 MeijerG[{{1/3, 5/6, 1 - 1/(3 r)}, {-(1/6), 1/6, 1/2}}, {{-1, -(1/3), 1, 5/3}, {-(1/6), 1/6, 1/2, -(1/(3 r))}}, (-(2/3)^(2/3)) a z^r, 1/3]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["BesselK", "[", RowBox[List["2", ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]], RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["8", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", "r"]]]]], RowBox[List["(", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "6"], ",", RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]]]], "}"]], ",", 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 MathML Form

 K 2 ( 2 3 ( a z r ) 3 / 2 ) Bi ( a z r ) z - 1 8 2 2 / 3 3 5 / 6 π 3 / 2 r ( z ( 4 π ( 3 log ( - a z r ) - 2 log ( ( a z r ) 3 / 2 ) ) G 4 , 6 2 , 3 ( - ( 2 3 ) 2 / 3 a z r , 1 3 1 3 , 5 6 , 1 - 1 3 r , 4 3 1 , 5 3 , - 1 , - 1 3 , 4 3 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["2", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[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[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["4", "3"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["4", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + G 4 , 6 4 , 3 ( - ( 2 3 ) 2 / 3 a z r , 1 3 1 3 , 5 6 , 1 - 1 3 r , 11 6 - 1 , - 1 3 , 1 , 5 3 , 11 6 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["4", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[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[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["11", "6"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["11", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + 2 G 4 , 6 4 , 3 ( - ( 2 3 ) 2 / 3 a z r , 1 3 1 3 , 5 6 , 1 - 1 3 r , - 1 6 - 1 , - 1 3 , 1 , 5 3 , - 1 6 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["4", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[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[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "6"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "6"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + G 4 , 6 4 , 3 ( - ( 2 3 ) 2 / 3 a z r , 1 3 1 3 , 5 6 , 1 - 1 3 r , - 13 6 - 1 , - 1 3 , 1 , 5 3 , - 13 6 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["4", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[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[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["13", "6"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["13", "6"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] + 4 π 2 G 6 , 8 4 , 3 ( - ( 2 3 ) 2 / 3 a z r , 1 3 1 3 , 5 6 , 1 - 1 3 r , - 1 6 , 1 6 , 1 2 - 1 , - 1 3 , 1 , 5 3 , - 1 6 , 1 6 , 1 2 , - 1 3 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["6", ",", "8"]], RowBox[List["4", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[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[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "6"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "6"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", RowBox[List["3", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] ) ) z BesselK 2 2 3 a z r 3 2 AiryBiPrime a z r -1 1 8 2 2 3 3 5 6 3 2 r -1 z 4 3 -1 a z r -1 2 a z r 3 2 MeijerG 1 3 5 6 1 -1 1 3 r -1 4 3 1 5 3 -1 -1 1 3 4 3 -1 1 3 r -1 -1 2 3 2 3 a z r 1 3 MeijerG 1 3 5 6 1 -1 1 3 r -1 11 6 -1 -1 1 3 1 5 3 11 6 -1 1 3 r -1 -1 2 3 2 3 a z r 1 3 2 MeijerG 1 3 5 6 1 -1 1 3 r -1 -1 1 6 -1 -1 1 3 1 5 3 -1 1 6 -1 1 3 r -1 -1 2 3 2 3 a z r 1 3 MeijerG 1 3 5 6 1 -1 1 3 r -1 -1 13 6 -1 -1 1 3 1 5 3 -1 13 6 -1 1 3 r -1 -1 2 3 2 3 a z r 1 3 4 2 MeijerG 1 3 5 6 1 -1 1 3 r -1 -1 1 6 1 6 1 2 -1 -1 1 3 1 5 3 -1 1 6 1 6 1 2 -1 1 3 r -1 -1 2 3 2 3 a z r 1 3 [/itex]

 Rule Form

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

 2001-10-29