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http://functions.wolfram.com/01.05.27.0006.01
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Log[z^(1/a), z] == (a Log[z])/(2 I a Pi Floor[(Pi - Im[Log[z]/a])/(2 Pi)] +
Log[z])
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Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List[SuperscriptBox["z", FractionBox["1", "a"]], ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", FractionBox[RowBox[List["Log", "[", "z", "]"]], "a"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["Log", "[", "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> <msub> <mi> log </mi> <msup> <mi> z </mi> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> a </mi> </mrow> </msup> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mi> a </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <log /> <logbase> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </logbase> <ci> z </ci> </apply> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <imaginaryi /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <apply> <ln /> <ci> z </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List[SuperscriptBox["z_", FractionBox["1", "a_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", FractionBox[RowBox[List["Log", "[", "z", "]"]], "a"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["Log", "[", "z", "]"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
