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variants of this functions
Log






Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Series representations > Generalized power series > Expansions of log(1+z) at z==0 > Expansions of log(f(z)) at z==0





http://functions.wolfram.com/01.04.06.0032.01









  


  










Input Form





Log[f[z]] \[Proportional] 2 I Pi Floor[(Pi - Arg[Subscript[c, 0]] - Arg[f[z]/Subscript[c, 0]])/ (2 Pi)] + Log[Subscript[c, 0]] + (Subscript[c, 1]/Subscript[c, 0]) z + (Subscript[c, 2]/Subscript[c, 0] - Subscript[c, 1]^2/ (2 Subscript[c, 0]^2)) z^2 + (Subscript[c, 1]^3/(3 Subscript[c, 0]^3) - (Subscript[c, 1] Subscript[c, 2])/Subscript[c, 0]^2 + Subscript[c, 3]/Subscript[c, 0]) z^3 + \[Ellipsis] /; (z -> 0) && f[z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] && Subscript[c, 0] != 0










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> f </ci> <ci> z </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["f", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Arg", "[", SubscriptBox["c", "0"], "]"]], "-", RowBox[List["Arg", "[", FractionBox[RowBox[List["f", "[", "z", "]"]], SubscriptBox["c", "0"]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["Log", "[", SubscriptBox["c", "0"], "]"]], "+", FractionBox[RowBox[List[SubscriptBox["c", "1"], " ", "z"]], SubscriptBox["c", "0"]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[SubscriptBox["c", "2"], SubscriptBox["c", "0"]], "-", FractionBox[SubsuperscriptBox["c", "1", "2"], RowBox[List["2", " ", SubsuperscriptBox["c", "0", "2"]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[SubsuperscriptBox["c", "1", "3"], RowBox[List["3", " ", SubsuperscriptBox["c", "0", "3"]]]], "-", FractionBox[RowBox[List[SubscriptBox["c", "1"], " ", SubscriptBox["c", "2"]]], SubsuperscriptBox["c", "0", "2"]], "+", FractionBox[SubscriptBox["c", "3"], SubscriptBox["c", "0"]]]], ")"]], " ", SuperscriptBox["z", "3"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List[RowBox[List["(", RowBox[List["z", "\[Rule]", "0"]], ")"]], "&&", RowBox[List[RowBox[List["f", "[", "z", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubscriptBox["c", "k"], " ", SuperscriptBox["z", "k"]]]]]]], "&&", RowBox[List[SubscriptBox["c", "0"], "\[NotEqual]", "0"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





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