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ArcCsc




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Representations through more general functions > Through Meijer G > Generalized cases for the direct function itself





http://functions.wolfram.com/01.17.26.0036.01









  


  








Input Form





ArcCsc[z] + (z/2) Sqrt[-(1/z^2)] Log[-(4/z^2)] - (z/2) Sqrt[-(1/z^2)] Sum[(Pochhammer[1/2, k] z^(2 k))/(k k!), {k, 1, n}] == (((-1)^(n - 1) z)/(2 Sqrt[Pi])) Sqrt[-(1/z^2)] MeijerG[{{1/2, 1, 1 + n}, {}}, {{1 + n}, {0, 0}}, I z, 1/2] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{-Infinity, -1}], z] && !IntervalMemberQ[Interval[{1, Infinity}], z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCsc", "[", "z_", "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", "z_", " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z_", "2"]]]]], " ", RowBox[List["Log", "[", RowBox[List["-", FractionBox["4", SuperscriptBox["z_", "2"]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", "z_", " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z_", "2"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k_"]], "]"]], " ", SuperscriptBox["z_", RowBox[List["2", " ", "k_"]]]]], RowBox[List["k_", " ", RowBox[List["k_", "!"]]]]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["n", "-", "1"]]], " ", "z"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List["1", "+", "n"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "+", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]]]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]], ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]


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





2003-08-21