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http://functions.wolfram.com/01.16.10.0001.01
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ArcCot[z] ==
1/
(z
(1 +
1/(z^2 (3 + 4/(z^2 (5 + 9/(z^2 (7 + 16/(z^2 (9 + 25/(z^2 (11 +
36/(z^2 (13 + \[Ellipsis])))))))))))))) /;
!IntervalMemberQ[Interval[{-1, 1}], I z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCot", "[", "z", "]"]], "\[Equal]", " ", FractionBox[SuperscriptBox["z", RowBox[List["-", "1"]]], RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["-", "2"]]], RowBox[List["3", "+", FractionBox[RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["5", "+", FractionBox[RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["7", "+", FractionBox[RowBox[List["16", " ", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["9", "+", FractionBox[RowBox[List["25", " ", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["11", "+", FractionBox[RowBox[List["36", " ", SuperscriptBox["z", RowBox[List["-", "2"]]]]], RowBox[List["13", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]], "/;", "\[InvisibleSpace]", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "]"]]]]]]
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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> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mtext> </mtext> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 9 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 11 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 13 </mn> <mo> + </mo> <mo> … </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mtext> ​ </mtext> <mi> z </mi> </mrow> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msup> <mi> cot </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mtext> </mtext> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 9 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 9 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 11 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 13 </mn> <mo> + </mo> <mo> … </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mtext> ​ </mtext> <mi> z </mi> </mrow> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCot", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", FractionBox["1", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["3", "+", FractionBox["4", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["5", "+", FractionBox["9", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["7", "+", FractionBox["16", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["9", "+", FractionBox["25", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["11", "+", FractionBox["36", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["13", "+", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]], ")"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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