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ArcCosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.20.0004.01









  


  








Input Form





D[ArcCosh[z], {z, \[Alpha]}] == (Sqrt[z - 1]/Sqrt[1 - z]) (Pi/(z^\[Alpha] (2 Gamma[1 - \[Alpha]])) - 2^(\[Alpha] - 1) Sqrt[Pi] z^(1 - \[Alpha]) HypergeometricPFQRegularized[{1/2, 1/2, 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["ArcCosh", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["z", "-", "1"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Alpha]"]], "]"]]]]], "-", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "1"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]


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





2001-10-29