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; }

 AiryBi

 http://functions.wolfram.com/03.06.21.0046.01

 Input Form

 Integrate[z^(\[Alpha] - 1) AiryBi[(-a) z^r] AiryBi[a z^r], z] == (1/(12 2^(2/3) 3^(1/3) Pi^(3/2) r)) (z^\[Alpha] (-8 Pi^2 MeijerG[{{1 - \[Alpha]/(6 r)}, {}}, {{2/3}, {0, 1/6, 1/3, -(\[Alpha]/(6 r))}}, (a z^r)/(2^(1/3) 3^(2/3)), 1/6] + 3 MeijerG[{{1 - \[Alpha]/(6 r)}, {1/6}}, {{0, 1/6, 1/3, 2/3}, {1/6, -(\[Alpha]/(6 r))}}, (a z^r)/(2^(1/3) 3^(2/3)), 1/6]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], " ", RowBox[List["AiryBi", "[", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["z", "r"]]], "]"]], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["12", " ", SuperscriptBox["2", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", "r"]]], RowBox[List["(", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["2", "3"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "6"], ",", FractionBox["1", "3"], ",", RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], ",", FractionBox["1", "6"]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "6"], ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], ",", FractionBox["1", "6"]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z α - 1 Bi ( - a z r ) Bi ( a z r ) z z α 12 2 2 / 3 3 3 π 3 / 2 r ( 3 G 2 , 6 4 , 1 ( a z r 2 3 3 2 / 3 , 1 6 1 - α 6 r , 1 6 0 , 1 6 , 1 3 , 2 3 , 1 6 , - α 6 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "6"]], RowBox[List["4", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[RadicalBox["2", "3"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] - 8 π 2 G 1 , 5 1 , 1 ( a z r 2 3 3 2 / 3 , 1 6 1 - α 6 r 2 3 , 0 , 1 6 , 1 3 , - α 6 r ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "5"]], RowBox[List["1", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[RadicalBox["2", "3"], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[TagBox[RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[FractionBox["2", "3"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "6"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] ) z z α -1 AiryBi -1 a z r AiryBi a z r z α 12 2 2 3 3 1 3 3 2 r -1 3 MeijerG 1 -1 α 6 r -1 1 6 0 1 6 1 3 2 3 1 6 -1 α 6 r -1 a z r 2 1 3 3 2 3 -1 1 6 -1 8 2 MeijerG 1 -1 α 6 r -1 2 3 0 1 6 1 3 -1 α 6 r -1 a z r 2 1 3 3 2 3 -1 1 6 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["AiryBi", "[", RowBox[List[RowBox[List["-", "a_"]], " ", SuperscriptBox["z_", "r_"]]], "]"]], " ", RowBox[List["AiryBi", "[", RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["2", "3"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "6"], ",", FractionBox["1", "3"], ",", RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], ",", FractionBox["1", "6"]]], "]"]]]], "+", RowBox[List["3", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "6"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "6"], ",", FractionBox["1", "3"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", RowBox[List["-", FractionBox["\[Alpha]", RowBox[List["6", " ", "r"]]]]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]]]]], ",", FractionBox["1", "6"]]], "]"]]]]]], ")"]]]], RowBox[List["12", " ", 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