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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Series representations > Generalized power series > Expansions at z==-i > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.29.06.0061.01









  


  










Input Form





ArcCsch[z]^2 == -(Pi^2/4) + Sqrt[2] Pi Sqrt[I (z + I)] HypergeometricPFQ[{{3/2}, {1/2}, {1/2}}, {{}, {3/2}, {3/2}}, -1, (-I) (z + I)] - 2 I (z + I) HypergeometricPFQ[{{3/2}, {1/2}, {1/2}}, {{}, {3/2}, {3/2}}, -1, (-I) (z + I)]^2










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcCsch", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], "4"]]], "+", RowBox[List[SqrtBox["2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]]]], "}"]], ",", RowBox[List["-", "1"]], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]], ",", RowBox[List["{", FractionBox["3", "2"], "}"]]]], "}"]], ",", RowBox[List["-", "1"]], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]]]], "]"]], "2"]]]]]]]]]










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





2007-05-02





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