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 KelvinKei

 http://functions.wolfram.com/03.19.06.0047.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["5", "/", "8"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", "z"]]]]]], RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "4"]]]], List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", 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"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", "z"]]]]]]]], RowBox[List[FractionBox["\[Pi]", "4"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["3", " ", "\[Pi]"]], "4"]]]], List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", 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"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", "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[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]]]

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

 2007-05-02