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ArcCos




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCos[z] > Representations through more general functions > Through Meijer G > Generalized cases for powers of cos-1





http://functions.wolfram.com/01.13.26.0040.01









  


  








Input Form





ArcCos[z]^2 == Pi^2/4 + ((I Sqrt[Pi])/2) MeijerG[{{1, 1}, {}}, {{1/2}, {0}}, I z, 1/2] - (Sqrt[Pi]/2) MeijerG[{{1, 1, 1}, {}}, {{1}, {0, 1/2}}, I 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["ArcCos", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]]]]]]]]


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





2003-08-21