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 KelvinKer

 http://functions.wolfram.com/03.20.06.0020.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], ",", " ", RowBox[List["\[Nu]", "\[Equal]", "0"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["Abs", "[", "\[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["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], ",", RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], ",", 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"], "]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "+", "2"]], "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["Abs", "[", "\[Nu]", "]"]], "-", "2"]], ")"]], "!"]]]], ",", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], ",", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]]]]]]

 MathML Form

 ker ν ( z ) - log ( z ) ν 0 ( - 1 ) "\[LeftBracketingBar]" ν "\[RightBracketingBar]" 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 z - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ) ! ν 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ( - 1 ) θ UnitStep ( ν - 1 4 ) ( - 1 ) ν - 1 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 3 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 + 2 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 3 z 2 - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 2 ) ! ν - 2 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] - ( - 1 ) θ UnitStep ( ν - 3 4 ) ( - 1 ) ν - 3 4 2 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 3 2 z - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ) ! ν - 3 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] 2 ν - 1 cos ( 3 π ν 4 ) Γ ( ν ) z - ν + 2 - ν - 1 cos ( π ν 4 ) Γ ( - ν ) z ν True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( z "\[Rule]" 0 ) Condition Proportional KelvinKer ν z -1 z ν 0 -1 ν 4 -1 2 ν -1 z -1 ν ν -1 ν 4 -1 -1 UnitStep ν -1 4 -1 -1 ν -1 4 -1 2 ν -1 3 2 z -1 ν ν -1 ν -1 4 -1 -1 UnitStep ν 2 4 -1 -1 ν 2 4 -1 2 ν -3 z 2 -1 ν ν -2 ν -2 4 -1 -1 -1 UnitStep ν -3 4 -1 -1 ν -3 4 -1 2 ν -1 3 2 z -1 ν ν -1 ν -3 4 -1 2 ν -1 3 ν 4 -1 Gamma ν z -1 ν 2 -1 ν -1 ν 4 -1 Gamma -1 ν z ν Rule z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], RowBox[List["\[Nu]", "\[Equal]", "0"]]], List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["Abs", "[", "\[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["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]]], List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], 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"], "]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "+", "2"]], "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["Abs", "[", "\[Nu]", "]"]], "-", "2"]], ")"]], "!"]]]], RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]]], List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["UnitStep", "[", FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "]"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", SuperscriptBox["z", RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]], ")"]], "!"]]]], RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]]], List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Nu]"]], "4"], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["-", "\[Nu]"]], "]"]]]]]], 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