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; }

 KelvinBer

 http://functions.wolfram.com/03.18.06.0021.01

 Input Form

 KelvinBer[\[Nu], z] \[Proportional] Piecewise[{{(((-1)^(\[Nu]/4) 2^\[Nu])/(z^\[Nu] (-\[Nu])!)) (1 + O[z^2]), Element[\[Nu]/4, Integers] && \[Nu] < 0}, {(((-1)^((\[Nu] - 1)/4) 2^(\[Nu] - 1/2))/(z^\[Nu] (-\[Nu])!)) (1 + O[z^2]), Element[(\[Nu] - 1)/4, Integers] && \[Nu] < 0}, {(((-1)^((\[Nu] + 2)/4) 2^(\[Nu] - 2) z^(2 - \[Nu]))/(1 - \[Nu])!) (1 + O[z^2]), Element[(\[Nu] - 2)/4, Integers] && \[Nu] < 0}, {(((-1)^((\[Nu] + 1)/4) 2^(\[Nu] - 1/2))/(z^\[Nu] (-\[Nu])!)) (1 + O[z^2]), Element[(\[Nu] - 3)/4, Integers] && \[Nu] < 0}}, ((z^\[Nu] Cos[(3 Pi \[Nu])/4])/(2^\[Nu] Gamma[1 + \[Nu]])) (1 + O[z^2])]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " "]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]], ",", RowBox[List[RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]], "&&", " ", RowBox[List["\[Nu]", "<", "0"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]]]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]], ",", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "\[Element]", "Integers"]], "&&", " ", RowBox[List["\[Nu]", "<", "0"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["(", RowBox[List["\[Nu]", "+", "2"]], ")"]], "4"]], SuperscriptBox["2", RowBox[List["\[Nu]", "-", "2"]]], " ", SuperscriptBox["z", RowBox[List["2", "-", "\[Nu]"]]], " "]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], "!"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]], ",", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]], "&&", " ", RowBox[List["\[Nu]", "<", "0"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "+", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]]]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]], ",", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]], "&&", " ", RowBox[List["\[Nu]", "<", "0"]]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]]]], "]"]]]]]]

 MathML Form

 ber ν ( z ) ( - 1 ) ν / 4 2 ν z - ν ( - ν ) ! ( 1 + O ( z 2 ) ) ν 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ν < 0 ( - 1 ) ν - 1 4 2 ν - 1 2 z - ν ( - ν ) ! ( 1 + O ( z 2 ) ) ν - 1 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ν < 0 ( - 1 ) ν + 2 4 2 ν - 2 z 2 - ν ( 1 - ν ) ! ( 1 + O ( z 2 ) ) ν - 2 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ν < 0 ( - 1 ) ν + 1 4 2 ν - 1 2 z - ν ( - ν ) ! ( 1 + O ( z 2 ) ) ν - 3 4 TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] ν < 0 2 - ν z ν cos ( 3 π ν 4 ) Γ ( ν + 1 ) ( 1 + O ( z 2 ) ) True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] Proportional KelvinBer ν z -1 ν 4 -1 2 ν z -1 ν -1 ν -1 1 O z 2 ν 4 -1 ν 0 -1 ν -1 4 -1 2 ν -1 1 2 z -1 ν -1 ν -1 1 O z 2 ν -1 4 -1 ν 0 -1 ν 2 4 -1 2 ν -2 z 2 -1 ν 1 -1 ν -1 1 O z 2 ν -2 4 -1 ν 0 -1 ν 1 4 -1 2 ν -1 1 2 z -1 ν -1 ν -1 1 O z 2 ν -3 4 -1 ν 0 2 -1 ν z ν 3 ν 4 -1 Gamma ν 1 -1 1 O z 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[Piecewise]", GridBox[List[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["\[Nu]", "/", "4"]]], " ", SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List[RowBox[List[FractionBox["\[Nu]", "4"], "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "<", "0"]]]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "1"]], "4"], "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "<", "0"]]]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "+", "2"]], "4"]], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "-", "2"]]], " ", SuperscriptBox["z", RowBox[List["2", "-", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], "!"]]], RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "2"]], "4"], "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "<", "0"]]]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], FractionBox[RowBox[List["\[Nu]", "+", "1"]], "4"]], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], "!"]]], RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "3"]], "4"], "\[Element]", "Integers"]], "&&", RowBox[List["\[Nu]", "<", "0"]]]]], List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[Nu]"]], "4"], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]]]]]]

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

 2007-05-02