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http://functions.wolfram.com/01.28.27.1634.01
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ArcCoth[Sqrt[z]] == (I/2) ArcSec[(z - 1)/(z + 1)] /; Im[z] < 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["ArcSec", "[", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arccoth /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <imaginaryi /> <apply> <arcsec /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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