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ArcCsc




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions





http://functions.wolfram.com/01.17.26.0011.01









  


  








Input Form





(1/Sqrt[z - 1]) ArcCsc[1/Sqrt[z]] == (Sqrt[Pi]/2) MeijerG[{{1/2, 1/2}, {}}, {{1/2}, {0}}, -z] /; !IntervalMemberQ[Interval[{0, 1}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[FractionBox["1", RowBox[List[" ", SqrtBox[RowBox[List["z", "-", "1"]]]]]], RowBox[List["ArcCsc", "[", FractionBox["1", SqrtBox["z"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[SqrtBox["\[Pi]"], "2"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["ArcCsc", "[", FractionBox["1", SqrtBox["z_"]], "]"]], SqrtBox[RowBox[List["z_", "-", "1"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29