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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Series representations > Generalized power series > Expansions at z==-1 > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.30.06.0090.01









  


  










Input Form





ArcSech[z]^2 == -Pi^2 + 4 Pi Sqrt[-z - 1] Sum[(Pochhammer[1/2, k]/k!) Hypergeometric2F1[1/2, 3/2 + k, 3/2, -1] (z + 1)^k, {k, 0, Infinity}] + 4 (z + 1) Sum[(Pochhammer[1/2, k]/k!) Hypergeometric2F1[1/2, 3/2 + k, 3/2, -1] (z + 1)^k, {k, 0, Infinity}]^2 /; Abs[z + 1] < 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["ArcSech", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List["4", " ", "\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", "k"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "1"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "+", "k"]], ",", FractionBox["3", "2"], ",", RowBox[List["-", "1"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], "k"]]], RowBox[List["k", "!"]]]]], ")"]], "2"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["z", "+", "1"]], "]"]], "<", "2"]]]]]]]]










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





2007-05-02