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variants of this functions
LegendreP






Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,mu,2,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/05.07.20.0009.01









  


  










Input Form





D[LegendreP[n, \[Mu], 2, z], {z, m}] == Sqrt[Pi] Sum[((-1)^(m - k) (1 - z^2)^((k - m)/2) Binomial[m, k] Pochhammer[-\[Mu] - n, m - k] HypergeometricPFQRegularized[ {1, -k, \[Mu]/2}, {(1 - k)/2, 1 - k/2}, z^2/(z^2 - 1)] Pochhammer[1 - \[Mu] + n, m - k] LegendreP[n, k - m + \[Mu], 2, z])/ z^k, {k, 0, m}] /; Element[m, Integers] && m >= 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "m_"]], "}"]]]]], RowBox[List["LegendreP", "[", RowBox[List["n_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "m"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "-", "k"]]], " ", SuperscriptBox["z", RowBox[List["-", "k"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], ")"]], FractionBox[RowBox[List["k", "-", "m"]], "2"]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[Mu]"]], "-", "n"]], ",", RowBox[List["m", "-", "k"]]]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", "k"]], ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k"]], "2"], ",", RowBox[List["1", "-", FractionBox["k", "2"]]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "\[Mu]", "+", "n"]], ",", RowBox[List["m", "-", "k"]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", RowBox[List["k", "-", "m", "+", "\[Mu]"]], ",", "2", ",", "z"]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02