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ArcCsc






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Representations through equivalent functions > With related functions > Involving tan-1 > Involving csc-1((a2 z2 c+1)1/2/a zc) > Involving csc-1((a2 z2 c+1)1/2/a zc) and tan-1(a zc)





http://functions.wolfram.com/01.17.27.0019.02









  


  










Input Form





ArcCsc[Sqrt[a^2 z^(2 c) + 1]/(a z^c)] == (Pi/2) (Sqrt[1/(1 - I a z^c)] Sqrt[1 - I a z^c] - Sqrt[1/(I a z^c + 1)] Sqrt[I a z^c + 1]) + ArcTan[a z^c] Sqrt[1/(a^2 z^(2 c) + 1)] Sqrt[a^2 z^(2 c) + 1]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCsc", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List[SuperscriptBox["a_", "2"], " ", SuperscriptBox["z_", RowBox[List["2", " ", "c_"]]]]], "+", "1"]]], RowBox[List["a_", " ", SuperscriptBox["z_", "c_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[FractionBox["1", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", SuperscriptBox["z", "c"]]]]]]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", "a", " ", SuperscriptBox["z", "c"]]]]]]]], "-", RowBox[List[SqrtBox[FractionBox["1", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", SuperscriptBox["z", "c"]]], "+", "1"]]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", SuperscriptBox["z", "c"]]], "+", "1"]]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List["a", " ", SuperscriptBox["z", "c"]]], "]"]], " ", SqrtBox[FractionBox["1", RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "c"]]]]], "+", "1"]]]], " ", SqrtBox[RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "c"]]]]], "+", "1"]]]]]]]]]]]










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





2001-10-29