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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.29.06.0042.01









  


  










Input Form





ArcCsch[z]^2 == 2 Log[2]^2 + (1/4) Log[1/z^2]^2 + Log[1/(4 z^2)] Log[1 + Sqrt[1 + z^2]] + Log[1 + Sqrt[1 + z^2]]^2 - 2 PolyLog[2, 1/2 - (1/2) Sqrt[1 + z^2]] - (z^2/4) Sum[(-1)^k Pochhammer[3/2, k] ((PolyGamma[-(1/2) - k] - PolyGamma[k + 1])/((k + 1)^2 k!)) z^(2 k), {k, 0, Infinity}] /; Abs[z] < 1










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[RowBox[List["2", " ", SuperscriptBox[RowBox[List["Log", "[", "2", "]"]], "2"]]], "+", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["Log", "[", FractionBox["1", SuperscriptBox["z", "2"]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["Log", "[", FractionBox["1", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]], "]"]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]], "]"]]]], "+", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]], "]"]], "2"], "-", RowBox[List["2", " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "2"]]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "k"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["k", "+", "1"]], "]"]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", " ", "k"]]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], "2"], " ", RowBox[List["k", "!"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]










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





2007-05-02





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