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/03.08.26.0017.01

 Input Form

 AiryBiPrime[z] BesselK[\[Nu], (2 z^(3/2))/3] == ((3^(1/6) Pi^(3/2) Csc[Pi \[Nu]])/2^(2/3)) (MeijerG[{{1/3, 5/6}, {1/3 - \[Nu]/2, 5/6 - \[Nu]/2}}, {{-(\[Nu]/2), 2/3 - \[Nu]/2}, {1/3 - \[Nu]/2, 5/6 - \[Nu]/2, \[Nu]/2, 2/3 + \[Nu]/2}}, (2/3)^(2/3) z, 1/3] - MeijerG[{{1/3, 5/6}, {1/3 + \[Nu]/2, 5/6 + \[Nu]/2}}, {{\[Nu]/2, 2/3 + \[Nu]/2}, {-(\[Nu]/2), 2/3 - \[Nu]/2, 1/3 + \[Nu]/2, 5/6 + \[Nu]/2}}, (2/3)^(2/3) z, 1/3]) /; Inequality[-((2 Pi)/3), Less, Arg[z], LessEqual, (2 Pi)/3]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["AiryBiPrime", "[", "z", "]"]], " ", RowBox[List["BesselK", "[", RowBox[List["\[Nu]", ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], SuperscriptBox["2", RowBox[List["2", "/", "3"]]]], 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["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"], ",", RowBox[List[FractionBox["2", "3"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], ",", FractionBox["1", "3"]]], "]"]], "-", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Nu]", "2"], ",", RowBox[List[FractionBox["2", "3"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "3"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], ",", FractionBox["1", "3"]]], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", "\[Pi]"]], "3"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", "\[Pi]"]], "3"]]]]]]]

 MathML Form

 Bi ( z ) K ν ( 2 z 3 / 2 3 ) 3 6 π 3 / 2 csc ( π ν ) 2 2 / 3 ( G 4 , 6 2 , 2 ( ( 2 3 ) 2 / 3 z , 1 3 1 3 , 5 6 , 1 3 - ν 2 , 5 6 - ν 2 - ν 2 , 2 3 - ν 2 , 1 3 - ν 2 , 5 6 - ν 2 , ν 2 , ν 2 + 2 3 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], 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[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["\[Nu]", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["2", "3"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] - G 4 , 6 2 , 2 ( ( 2 3 ) 2 / 3 z , 1 3 1 3 , 5 6 , ν 2 + 1 3 , ν 2 + 5 6 ν 2 , ν 2 + 2 3 , - ν 2 , 2 3 - ν 2 , ν 2 + 1 3 , ν 2 + 5 6 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], 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[FractionBox["\[Nu]", "2"], "+", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["5", "6"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox["\[Nu]", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["2", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["1", "3"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "+", FractionBox["5", "6"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] ) /; - 2 π 3 < arg ( z ) 2 π 3 Condition Bi z Subscript K ν 2 z 3 2 3 -1 3 1 6 3 2 csc ν 2 2 3 -1 MeijerG 1 3 5 6 1 3 -1 ν 2 -1 5 6 -1 ν 2 -1 -1 ν 2 -1 2 3 -1 ν 2 -1 1 3 -1 ν 2 -1 5 6 -1 ν 2 -1 ν 2 -1 ν 2 -1 2 3 2 3 2 3 z 1 3 -1 MeijerG 1 3 5 6 ν 2 -1 1 3 ν 2 -1 5 6 ν 2 -1 ν 2 -1 2 3 -1 ν 2 -1 2 3 -1 ν 2 -1 ν 2 -1 1 3 ν 2 -1 5 6 2 3 2 3 z 1 3 Inequality -1 2 3 -1 z 2 3 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["AiryBiPrime", "[", "z_", "]"]], " ", RowBox[List["BesselK", "[", RowBox[List["\[Nu]_", ",", FractionBox[RowBox[List["2", " ", SuperscriptBox["z_", RowBox[List["3", "/", "2"]]]]], "3"]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["3", RowBox[List["1", "/", "6"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], " ", 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["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"], ",", RowBox[List[FractionBox["2", "3"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], ",", FractionBox["1", "3"]]], "]"]], "-", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "6"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "3"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Nu]", "2"], ",", RowBox[List[FractionBox["2", "3"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["2", "3"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "3"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["5", "6"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["2", "/", "3"]]], " ", "z"]], ",", FractionBox["1", "3"]]], "]"]]]], ")"]]]], SuperscriptBox["2", RowBox[List["2", "/", "3"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "3"]]], " ", RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["2", " ", "\[Pi]"]], "3"]]]]]]]]]

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

 2001-10-29