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 WhittakerM

 http://functions.wolfram.com/07.44.20.0004.01

 Input Form

 Derivative[0, 1, 0][WhittakerM][\[Nu], \[Mu], z] == Log[z] WhittakerM[\[Nu], \[Mu], z] + (z^(1/2 + \[Mu]) ((-((z (1 + 2 \[Mu] - 2 \[Nu]))/(1 + 2 \[Mu])^2)) HypergeometricPFQ[{{3/2 + \[Mu] - \[Nu]}, {1}, {1, 1 + 2 \[Mu]}}, {{2, 2 + 2 \[Mu]}, {}, {2 + 2 \[Mu]}}, z, z] + (z/(1 + 2 \[Mu])) HypergeometricPFQ[{{3/2 + \[Mu] - \[Nu]}, {1}, {1, 1/2 + \[Mu] - \[Nu]}}, {{2, 2 + 2 \[Mu]}, {}, {3/2 + \[Mu] - \[Nu]}}, z, z]))/E^(z/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Derivative", "[", RowBox[List["0", ",", "1", ",", "0"]], "]"]], "[", "WhittakerM", "]"]], "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "z"]], "/", "2"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", "\[Mu]"]], "-", RowBox[List["2", "\[Nu]"]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]], "2"], " "]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox["z", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]]]], ")"]]]]]]]]]]

 MathML Form

 M TagBox["M", BesselJ] ν , μ ( 0 , 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "0"]], ")"]], Derivative] ( z ) - z 2 ( z 2 μ + 1 F 2 , 0 , 1 1 , 1 , 2 ( μ - ν + 3 2 ; 1 ; 1 , μ - ν + 1 2 ; 2 , 2 μ + 2 ; ; μ - ν + 1 2 ; z , z ) - 1 ( 2 μ + 1 ) 2 ( z ( 2 μ - 2 ν + 1 ) ) F 2 , 0 , 1 1 , 1 , 2 ( μ - ν + 3 2 ; 1 ; 1 , 2 μ + 1 ; 2 , 2 μ + 2 ; ; 2 μ + 2 ; z , z ) ) z μ + 1 2 + log ( z ) M TagBox["M", WhittakerM] ν , μ ( z ) FormBox RowBox RowBox SubsuperscriptBox TagBox M BesselJ RowBox ν , μ TagBox RowBox ( RowBox 0 , 1 , 0 ) Derivative ( z ) RowBox RowBox SuperscriptBox RowBox - FractionBox z 2 RowBox ( RowBox RowBox FractionBox z RowBox RowBox 2 μ + 1 RowBox SubsuperscriptBox F RowBox 2 , 0 , 1 RowBox 1 , 1 , 2 [ RowBox RowBox GridBox RowBox RowBox RowBox μ - ν + FractionBox 3 2 ; 1 ; 1 , RowBox RowBox μ - ν + FractionBox 1 2 ; RowBox 2 , RowBox RowBox RowBox RowBox 2 μ + 2 RowBox ; ; RowBox μ - ν + FractionBox 1 2 ; z , z ] - RowBox FractionBox 1 SuperscriptBox RowBox ( RowBox RowBox 2 μ + 1 ) 2 RowBox ( RowBox z RowBox ( RowBox RowBox 2 μ - RowBox 2 ν + 1 ) ) RowBox SubsuperscriptBox F RowBox 2 , 0 , 1 RowBox 1 , 1 , 2 ( RowBox RowBox GridBox RowBox RowBox RowBox μ - ν + FractionBox 3 2 ; 1 ; 1 , RowBox RowBox RowBox 2 μ + 1 ; RowBox 2 , RowBox RowBox RowBox RowBox 2 μ + 2 RowBox ; ; RowBox RowBox 2 μ + 2 ; z , z ) ) SuperscriptBox z RowBox μ + FractionBox 1 2 + RowBox RowBox log ( z ) RowBox SubscriptBox TagBox M WhittakerM RowBox ν , μ ( z ) TraditionalForm [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["WhittakerM", TagBox[RowBox[List["(", RowBox[List["0", ",", "1", ",", "0"]], ")"]], Derivative], Rule[MultilineFunction, None]], "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "2"]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]], "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]], "2"]]]], "+", FractionBox[RowBox[List["z", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "+", RowBox[List["2", " ", "\[Mu]"]]]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]]]], "}"]], ",", "z", ",", "z"]], "]"]]]], RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]]]]], ")"]]]]]]]]]]

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

 2007-05-02

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