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http://functions.wolfram.com/01.13.27.1900.01
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ArcCos[z] == Pi + (Pi Sqrt[-1 - z] Sqrt[1/z] Sqrt[-z])/Sqrt[1 + z] +
2 Sqrt[1/z] Sqrt[-(z/(1 + z))] Sqrt[1 + z] ArcCoth[Sqrt[(z + 1)/(z - 1)]]
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Cell[BoxData[RowBox[List[RowBox[List["ArcCos", "[", "z", "]"]], "\[Equal]", RowBox[List["\[Pi]", "+", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List["-", "z"]]]]], SqrtBox[RowBox[List["1", "+", "z"]]]], "+", RowBox[List["2", " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List["-", FractionBox["z", RowBox[List["1", "+", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]]], "]"]]]]]]]]]]
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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> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> π </mi> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mtext> </mtext> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arccos /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arccoth /> <apply> <power /> <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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <pi /> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCos", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[Pi]", "+", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List["-", "z"]]]]], SqrtBox[RowBox[List["1", "+", "z"]]]], "+", RowBox[List["2", " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[RowBox[List["-", FractionBox["z", RowBox[List["1", "+", "z"]]]]]], " ", SqrtBox[RowBox[List["1", "+", "z"]]], " ", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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