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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,2,z] > Differentiation > Low-order differentiation > With respect to nu





http://functions.wolfram.com/07.08.20.0003.01









  


  










Input Form





D[LegendreP[\[Nu], \[Mu], 2, z], \[Nu]] == (-((2 \[Nu] + 1)/(2 Gamma[2 - \[Mu]]))) ((1 + z)^(\[Mu]/2)/ (1 - z)^(\[Mu]/2 - 1)) HypergeometricPFQ[{{1 - \[Nu], 2 + \[Nu]}, {1}, {1, -\[Nu], 1 + \[Nu]}}, {{2, 2 - \[Mu]}, {}, {2 + \[Nu], 1 - \[Nu]}}, (1 - z)/2, (1 - z)/2]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "\[Nu]"], RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "1"]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Mu]"]], "]"]]]]]]], " ", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[RowBox[List["\[Mu]", "/", "2"]], "-", "1"]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", "\[Nu]"]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "-", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["\[Nu]_"]]], RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", "\[Nu]"]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "-", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Mu]"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[FractionBox["\[Mu]", "2"], "-", "1"]]]]]]]]]]]]










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





2001-10-29





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