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ArcCsc




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.17.26.0034.01









  


  








Input Form





ArcCsc[Sqrt[z]] + (Sqrt[z]/2) Sqrt[-(1/z)] Log[-(4/z)] - (Sqrt[z]/2) Sqrt[-(1/z)] Sum[(Pochhammer[1/2, k] z^k)/(k k!), {k, 1, n}] == (((-1)^(n - 1) Sqrt[z])/(2 Sqrt[Pi])) Sqrt[-(1/z)] MeijerG[{{1/2, 1, 1 + n}, {}}, {{1 + n}, {0, 0}}, -z] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{0, 1}], 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", "[", SqrtBox["z_"], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["z_"], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z_"]]]], " ", RowBox[List["Log", "[", RowBox[List["-", FractionBox["4", "z_"]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["z_"], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z_"]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k_"]], "]"]], " ", SuperscriptBox["z_", "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"]]], " ", SqrtBox["z"]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", 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["-", "z"]]]], "]"]]]], 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["0", ",", "1"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]


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





2003-08-21