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ArcCosh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCosh[z] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/01.26.26.0009.01









  


  








Input Form





ArcCosh[z] == (1/2) Log[-4 z^2] - (Pi Sqrt[-z^2])/(2 z) - (1/(4 z^2)) HypergeometricPFQ[{1, 1, 3/2}, {2, 2}, 1/z^2] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["z", "2"]]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", " ", "z"]]], "-", FractionBox[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2"]], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]], RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29