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; }

 WhittakerM

 http://functions.wolfram.com/07.44.10.0001.01

 Input Form

 WhittakerM[\[Nu], \[Mu], z] == (z^(1/2 + \[Mu]) (1 + ((1/2 + \[Mu] - \[Nu]) z)/ ((2 \[Mu] + 1) (1 - ((3/2 + \[Mu] - \[Nu]) z)/(2 (2 \[Mu] + 2))/ (1 + ((3/2 + \[Mu] - \[Nu]) z)/(2 (2 \[Mu] + 2)) - ((5/2 + \[Mu] - \[Nu]) z)/(3 (2 \[Mu] + 3))/ (1 + ((5/2 + \[Mu] - \[Nu]) z)/(3 (2 \[Mu] + 3)) - ((7/2 + \[Mu] - \[Nu]) z)/(4 (2 \[Mu] + 4))/ (1 + ((7/2 + \[Mu] - \[Nu]) z)/(4 (2 \[Mu] + 4)) - ((9/2 + \[Mu] - \[Nu]) z)/(5 (2 \[Mu] + 5))/ (1 + ((9/2 + \[Mu] - \[Nu]) z)/(5 (2 \[Mu] + 5)) + \[Ellipsis]))))))))/E^(z/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], "/", "2"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "1"]]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["2", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "2"]], ")"]]]]]]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["2", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "2"]], ")"]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["5", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["3", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "3"]], ")"]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["5", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["3", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "3"]], ")"]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["7", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["4", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "4"]], ")"]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["7", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["4", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "4"]], ")"]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["9", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["5", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "5"]], ")"]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["9", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], "z"]], RowBox[List["5", RowBox[List["(", RowBox[List[RowBox[List["2", "\[Mu]"]], "+", "5"]], ")"]]]]], "+", "\[Ellipsis]"]]]]]]]]]]], ")"]]]]], ")"]]]]], ")"]]]]]]]]

 MathML Form

 M TagBox["M", WhittakerM] ν , μ ( z ) - z 2 z μ + 1 2 ( 1 + ( 1 2 + μ - ν ) z 2 μ + 1 ( 1 + - ( 3 2 + μ - ν ) z 2 ( 2 μ + 2 ) ( 1 + ( 3 2 + μ - ν ) z 2 ( 2 μ + 2 ) + - ( 5 2 + μ - ν ) z 3 ( 2 μ + 3 ) 1 + ( 5 2 + μ - ν ) z 3 ( 2 μ + 3 ) + - ( 7 2 + μ - ν ) z 4 ( 2 μ + 4 ) 1 + ( 7 2 + μ - ν ) z 4 ( 2 μ + 4 ) + - ( 9 2 + μ - ν ) z 5 ( 2 μ + 5 ) 1 + ( 9 2 + μ - ν ) z 5 ( 2 μ + 5 ) + ) ) ) WhittakerM ν μ z -1 z 2 -1 z μ 1 2 1 1 2 μ -1 ν z 2 μ 1 -1 1 -1 3 2 μ -1 ν z 2 2 μ 2 -1 1 3 2 μ -1 ν z 2 2 μ 2 -1 -1 5 2 μ -1 ν z 3 2 μ 3 -1 1 5 2 μ -1 ν z 3 2 μ 3 -1 -1 7 2 μ -1 ν z 4 2 μ 4 -1 1 7 2 μ -1 ν z 4 2 μ 4 -1 -1 9 2 μ -1 ν z 5 2 μ 5 -1 1 9 2 μ -1 ν z 5 2 μ 5 -1 -1 -1 -1 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "2"]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "2"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "2"]], ")"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["5", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "3"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["5", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "3"]], ")"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["7", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "4"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["7", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "4"]], ")"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["9", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "5"]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["9", "2"], "+", "\[Mu]", "-", "\[Nu]"]], ")"]], " ", "z"]], RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "5"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]]]

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

 2007-05-02