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ArcSec






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[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/01.18.06.0057.01









  


  










Input Form





ArcSec[z]^2 == Pi^2 - 2 Pi Sqrt[2] Sqrt[-z - 1] HypergeometricPFQ[{{3/2}, {1/2}, {1/2}}, {{}, {3/2}, {3/2}}, -1, z + 1] - 2 (z + 1) HypergeometricPFQ[{{3/2}, {1/2}, {1/2}}, {{}, {3/2}, {3/2}}, -1, 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["ArcSec", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[Pi]", "2"], "-", RowBox[List["2", " ", "\[Pi]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], " ", 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["z", "+", "1"]]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], " ", 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["z", "+", "1"]]]], "]"]], "2"]]]]]]]]]










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





2007-05-02