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http://functions.wolfram.com/01.04.10.0003.01
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Log[1 + z] ==
z/
(1 +
z/(2 + z/(3 + (2 z)/(2 + (2 z)/(5 + (3 z)/(2 + (3 z)/(7 +
\[Ellipsis]))))))) /;
!IntervalMemberQ[Interval[{-Infinity, -1}], z]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]], "\[Equal]", FractionBox["z", RowBox[List["1", "+", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["3", "+", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["2", "+", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["5", "+", FractionBox[RowBox[List["3", " ", "z"]], RowBox[List["2", "+", FractionBox[RowBox[List["3", " ", "z"]], RowBox[List["7", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]], "/;", FormBox[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]], "]"]], TraditionalForm]]]]]
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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> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mstyle scriptlevel='0'> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </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> </mstyle> </mrow> <mo> /; </mo> <mtext> ​ </mtext> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mstyle scriptlevel='0'> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mi> z </mi> <mstyle scriptlevel='0'> <mrow> <mn> 3 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 5 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mstyle scriptlevel='0'> <mrow> <mn> 7 </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> </mstyle> </mrow> <mo> /; </mo> <mtext> ​ </mtext> <mrow> <mi> z </mi> <mo> ∉ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ∞ </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["1", "+", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["z", RowBox[List["1", "+", FractionBox["z", RowBox[List["2", "+", FractionBox["z", RowBox[List["3", "+", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["2", "+", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["5", "+", FractionBox[RowBox[List["3", " ", "z"]], RowBox[List["2", "+", FractionBox[RowBox[List["3", " ", "z"]], RowBox[List["7", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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