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; }

 KelvinKei

 http://functions.wolfram.com/03.15.06.0023.01

 Input Form

 KelvinKei[z] \[Proportional] Piecewise[{{((-1)^(5/8) ((-1 + I) + Sqrt[2] E^(I Sqrt[2] z)) Sqrt[Pi])/ (4 E^((-1)^(1/4) z) Sqrt[z]), 4 Arg[z] <= Pi}, {Sqrt[Pi/2] ((-1)^(3/8)/(E^((-1)^(1/4) z) (2 Sqrt[z]))) (-1 + E^(I Sqrt[2] z) ((-1)^(1/4) - 2 I E^(Sqrt[2] z))), 4 Arg[z] <= 3 Pi}}, (((-1)^(5/8) Sqrt[Pi/2])/ (E^((-1)^(1/4) z) (2 Sqrt[z]))) ((-1)^(3/4) - 2 (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + 2 I E^(Sqrt[2] z))] /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKei", "[", "z", "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], "+", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", SqrtBox["\[Pi]"]]], RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]], " ", SqrtBox["z"]]]], ",", RowBox[List[RowBox[List["4", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " "]], RowBox[List["2", " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]]]], ")"]]]], ",", RowBox[List[RowBox[List["4", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", RowBox[List["3", " ", "\[Pi]"]]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox[FractionBox["\[Pi]", "2"]]]], RowBox[List["2", " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 kei ( z ) ( - 1 ) 5 / 8 ( ( - 1 + ) + 2 2 z ) π 4 - 1 4 z z 4 arg ( z ) π π 2 ( - 1 ) 3 / 8 - - 1 4 z 2 z ( 2 z ( - 1 4 - 2 2 z ) - 1 ) 4 arg ( z ) 3 π π 2 ( - 1 ) 5 / 8 - - 1 4 z 2 z ( ( - 1 ) 3 / 4 - 2 - 1 4 2 - 1 4 z + 2 z + 2 2 z ) True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinKei z -1 5 8 -1 2 1 2 2 1 2 z 1 2 4 -1 1 4 z z 1 2 -1 4 z 2 -1 1 2 -1 3 8 -1 -1 1 4 z 2 z 1 2 -1 2 1 2 z -1 1 4 -1 2 2 1 2 z -1 4 z 3 2 -1 1 2 -1 5 8 -1 -1 1 4 z 2 z 1 2 -1 -1 3 4 -1 2 -1 1 4 2 -1 1 4 z 2 1 2 z 2 2 1 2 z Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], "+", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", SqrtBox["\[Pi]"]]], RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]], " ", SqrtBox["z"]]]], RowBox[List[RowBox[List["4", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]], List[FractionBox[RowBox[List[SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["z"]]]], RowBox[List[RowBox[List["4", " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", RowBox[List["3", " ", "\[Pi]"]]]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox[FractionBox["\[Pi]", "2"]]]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], "-", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox["z"]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2007-05-02