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 KelvinKer

 http://functions.wolfram.com/03.16.06.0035.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", "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["1", "/", "8"]]], " ", 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["1", "/", "8"]]], " "]], RowBox[List["2", " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "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["1", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox["\[Pi]"]]], RowBox[List["4", " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", 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"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "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["1", "/", "8"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]]]]]], ")"]]]], RowBox[List["4", " ", 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