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ArcCoth




Mathematica Notation

Traditional Notation









Elementary Functions > ArcCoth[z] > Representations through equivalent functions > With related functions > Involving sech-1 > Involving coth-1((z2-1)1/2/z) > Involving coth-1((z2-1)1/2/z) and sech-1(1/z)





http://functions.wolfram.com/01.28.27.3489.01









  


  








Input Form





ArcCoth[Sqrt[z^2 - 1]/z] == ((Sqrt[-1 - z] Sqrt[z^2])/(Sqrt[-z^2] Sqrt[1 + z])) ArcSech[1/z] + (Sqrt[1 - z] Sqrt[1/(1 - z)] - (I Sqrt[1 - z^2])/Sqrt[-1 + z^2] - Sqrt[1 + z] Sqrt[1/(1 + z)]) ((Pi I)/2)








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> </msqrt> </mrow> <mo> - </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> - </mo> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], " ", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]]]], RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", "z"]]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["z", "2"]]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "+", "z"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]]]]]]]]


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





2003-09-04