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ArcCoth






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/01.28.20.0004.01









  


  










Input Form





D[ArcCoth[z], {z, \[Alpha]}] == 2^(\[Alpha] - 1) ((-((Pi z^(1 - \[Alpha]))/(2 Gamma[1 - \[Alpha]]))) Sqrt[-(1/z^2)] + z^(1 - \[Alpha]) Sqrt[Pi] HypergeometricPFQRegularized[{1/2, 1, 1}, {1 - \[Alpha]/2, 3/2 - \[Alpha]/2}, z^2])










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_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["ArcCoth", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "1"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]]]], "+", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]










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





2001-10-29





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