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; }

 KelvinBer

 http://functions.wolfram.com/03.18.26.0044.01

 Input Form

 (BesselI[\[Nu], (-1)^(1/4) z] - BesselI[-\[Nu], (-1)^(1/4) z]) KelvinBer[\[Nu], z] == (((Sqrt[Pi] Sin[Pi \[Nu]])/2) z^\[Nu] (Sqrt[2] Csc[Pi (3/4 + \[Nu])] E^((3 I Pi \[Nu])/4) MeijerG[{{1/2}, {1/4, \[Nu] - 1/4}}, {{0, \[Nu]}, {-\[Nu], 1/4, -(1/4) + \[Nu]}}, I z^2] - (1/(E^((3 I Pi \[Nu])/4) (2 Pi^2))) MeijerG[{{}, {}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2)}}, -(z^4/64)]))/ ((-1)^(1/4) z)^\[Nu] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, 0]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["\[Nu]", ",", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]], "]"]], "-", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]], "]"]]]], ")"]], RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], RowBox[List["2", " "]]], " ", SuperscriptBox["z", "\[Nu]"], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["-", "\[Nu]"]]], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["2"], RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox["3", "4"], "+", "\[Nu]"]], ")"]]]], "]"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", RowBox[List["\[Nu]", "-", FractionBox["1", "4"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], " ", ",", FractionBox["1", "4"], " ", ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "-", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]]]], RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "64"]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]

 MathML Form

 ( I ν ( - 1 4 z ) - I - ν ( - 1 4 z ) ) ber ν ( z ) 1 2 ( π sin ( π ν ) ) z ν ( - 1 4 z ) - ν ( 2 csc ( π ( ν + 3 4 ) ) 3 π ν 4 G 3 , 5 2 , 1 ( z 2 1 2 , 1 4 , ν - 1 4 0 , ν , - ν , 1 4 , ν - 1 4 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "5"]], RowBox[List["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Nu]", "-", FractionBox["1", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["\[Nu]", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", "\[Nu]"]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Nu]", "-", FractionBox["1", "4"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] - - 1 4 ( 3 π ν ) 2 π 2 G 0 , 4 3 , 0 ( - z 4 64 0 , 1 2 , ν 2 , - ν 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["0", ",", "4"]], RowBox[List["3", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "64"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Nu]", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) /; - π 2 < arg ( z ) 0 Condition BesselI ν -1 1 4 z -1 BesselI -1 ν -1 1 4 z KelvinBer ν z 1 2 1 2 ν z ν -1 1 4 z -1 ν 2 1 2 ν 3 4 3 ν 4 -1 MeijerG 1 2 1 4 ν -1 1 4 0 ν -1 ν 1 4 ν -1 1 4 z 2 -1 -1 1 4 3 ν 2 2 -1 MeijerG 0 1 2 ν 2 -1 -1 ν 2 -1 -1 z 4 64 -1 Inequality -1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z_"]]]], "]"]], "-", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z_"]]]], "]"]]]], ")"]], " ", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], " ", SuperscriptBox["z", "\[Nu]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["2"], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox["3", "4"], "+", "\[Nu]"]], ")"]]]], "]"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", RowBox[List["\[Nu]", "-", FractionBox["1", "4"]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", FractionBox["1", "4"], ",", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]], "]"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], ")"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "64"]]]]], "]"]]]], RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2007-05-02