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 KelvinKei

 http://functions.wolfram.com/03.19.06.0020.01

 Input Form

 KelvinKei[\[Nu], z] \[Proportional] Piecewise[{{-Pi/4, \[Nu] == 0}, {(-(-1)^(Abs[\[Nu]]/4)) 2^(-3 + Abs[\[Nu]]) z^(2 - Abs[\[Nu]]) (-2 + Abs[\[Nu]])!, Element[\[Nu]/4, Integers]}, {((-1 + I) (-1)^(\[Nu] - 1) (-1)^(\[Nu]/4) 2^(-2 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 1)/4, Integers]}, {((-1)^UnitStep[(\[Nu] - 2)/4] I (-1)^(\[Nu]/4) 2^(-1 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 2)/4, Integers]}, {((1 + I) (-1)^(\[Nu] - 1) (-1)^(\[Nu]/4) 2^(-2 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 3)/4, Integers]}}, (-2^(-1 - \[Nu])) z^\[Nu] Gamma[-\[Nu]] Sin[(Pi \[Nu])/4] - (2^(-1 + \[Nu]) Gamma[\[Nu]] Sin[(3 Pi \[Nu])/4])/z^\[Nu]] /; (z -> 0)

 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[RowBox[List["-", "\[Pi]"]], "/", "4"]], ",", " ", RowBox[List["\[Nu]", "\[Equal]", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "/", "4"]]]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], ",", RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], ",", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "\[Element]", "Integers"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "]"]]], "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], ",", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], ",", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]

 MathML Form

 kei ν ( z ) - π 4 ν 0 - ( - 1 ) "\[LeftBracketingBar]" ν "\[RightBracketingBar]" 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 3 z 2 - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 2 ) ! ν 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ( - 1 + ) ( - 1 ) ν - 1 ( - 1 ) ν / 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 2 z - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ) ! ν - 1 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ( - 1 ) θ UnitStep ( ν - 2 4 ) ( - 1 ) ν / 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 z - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ) ! ν - 2 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ( 1 + ) ( - 1 ) ν - 1 ( - 1 ) ν / 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 2 z - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ) ! ν - 3 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] - 2 ν - 1 Γ ( ν ) sin ( 3 π ν 4 ) z - ν - 2 - ν - 1 Γ ( - ν ) sin ( π ν 4 ) z ν True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( z "\[Rule]" 0 ) Condition Proportional KelvinKei ν z -1 4 -1 ν 0 -1 -1 ν 4 -1 2 ν -3 z 2 -1 ν ν -2 ν 4 -1 -1 -1 ν -1 -1 ν 4 -1 2 ν -2 z -1 ν ν -1 ν -1 4 -1 -1 UnitStep ν -2 4 -1 -1 ν 4 -1 2 ν -1 z -1 ν ν -1 ν -2 4 -1 1 -1 ν -1 -1 ν 4 -1 2 ν -2 z -1 ν ν -1 ν -3 4 -1 -1 2 ν -1 Gamma ν 3 ν 4 -1 z -1 ν -1 2 -1 ν -1 Gamma -1 ν ν 4 -1 z ν Rule z 0 [/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[RowBox[List["-", FractionBox["\[Pi]", "4"]]], RowBox[List["\[Nu]", "\[Equal]", "0"]]], List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "4"]]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["2", "-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]]], List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "\[Element]", "Integers"]]], List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "]"]]], " ", "\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]]], List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]], RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]]], List[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]]]

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

 2007-05-02