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ArcCsc






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.17.20.0004.01









  


  










Input Form





D[ArcCsc[z], {z, \[Alpha]}] == 2^(\[Alpha] - 3) Sqrt[Pi] Sqrt[-(1/z^2)] z^(3 - \[Alpha]) HypergeometricPFQRegularized[{1, 1, 3/2, 3/2}, {2, (3 - \[Alpha])/2, (4 - \[Alpha])/2}, z^2] - Sqrt[-(1/z^2)] (z^(1 - \[Alpha])/(2 Gamma[1 - \[Alpha]])) (2 EulerGamma + Log[-(4/z^2)] + 2 PolyGamma[1 - \[Alpha]])










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["ArcCsc", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "3"]]], " ", SqrtBox["\[Pi]"], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", SuperscriptBox["z", RowBox[List["3", "-", "\[Alpha]"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", FractionBox["3", "2"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"], ",", FractionBox[RowBox[List["4", "-", "\[Alpha]"]], "2"]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], "-", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "EulerGamma"]], "+", RowBox[List["Log", "[", RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]], "]"]], "+", RowBox[List["2", " ", RowBox[List["PolyGamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]]]]]]]]










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





2001-10-29





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