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ArcCos






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself





http://functions.wolfram.com/01.13.06.0064.01









  


  










Input Form





ArcCos[z] == Subscript[F, Infinity][z] /; Subscript[F, n][z] == Pi/2 - (z/(2 Sqrt[-z^2])) (Log[-4 z^2] - (1/(2 z^2)) Sum[Pochhammer[3/2, k]/ (z^(2 k) ((1 + k)^2 k!)), {k, 0, n}]) == ArcCos[z] - ((3 Pochhammer[5/2, n])/(z^(2 (2 + n)) (4 (2 + n)^2 (n + 1)!))) HypergeometricPFQ[{1, 5/2 + n, 2 + n}, {3 + n, 3 + n}, 1/z^2] && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["F", "\[Infinity]"], "[", "z", "]"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["F", "n"], "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox["z", "2"]]], "]"]], "-", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], " ", "k"]]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "k"]], ")"]], "2"], " ", RowBox[List["k", "!"]]]]]]], RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]], ")"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]]]]], "\[Equal]", RowBox[List[RowBox[List["ArcCos", "[", "z", "]"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["2", "+", "n"]], ")"]]]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "2"], ",", "n"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List[FractionBox["5", "2"], "+", "n"]], ",", RowBox[List["2", "+", "n"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["3", "+", "n"]], ",", RowBox[List["3", "+", "n"]]]], "}"]], ",", FractionBox["1", SuperscriptBox["z", "2"]]]], "]"]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", "+", "n"]], ")"]], "2"], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], "!"]]]]]]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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