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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/05.09.20.0008.01









  


  








Input Form





D[GegenbauerC[n, \[Lambda], z], {z, \[Alpha]}] == (((2^(1 - 2 \[Lambda]) Sqrt[Pi] Gamma[n + 2 \[Lambda]])/ (Gamma[n + 1] Gamma[\[Lambda]])) HypergeometricPFQRegularized[ {{-n, 2 \[Lambda] + n}, {1}, {}}, {{\[Lambda] + 1/2}, {1 - \[Alpha]}, {}}, -(z/2), 1/2])/z^\[Alpha]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["GegenbauerC", "[", RowBox[List["n", ",", " ", "\[Lambda]", ",", " ", "z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", RowBox[List["2", " ", "\[Lambda]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["n", "+", RowBox[List["2", " ", "\[Lambda]"]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]], SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List[RowBox[List["2", "\[Lambda]"]], "+", "n"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["\[Lambda]", "+", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "\[Alpha]"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", FractionBox["z", "2"]]], ",", FractionBox["1", "2"]]], "]"]]]]]]]]








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_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["GegenbauerC", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", RowBox[List["2", " ", "\[Lambda]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["n", "+", RowBox[List["2", " ", "\[Lambda]"]]]], "]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "n"]], ",", RowBox[List[RowBox[List["2", " ", "\[Lambda]"]], "+", "n"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["\[Lambda]", "+", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "\[Alpha]"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["-", FractionBox["z", "2"]]], ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", "\[Lambda]", "]"]]]]]]]]]


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





2001-10-29