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InverseJacobiND






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiND[z,m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/09.44.06.0003.02









  


  










Input Form





InverseJacobiND[z, m] \[Proportional] ((-(I/2)) (1 + m/4 + (9 m^2)/64 + \[Ellipsis]) Log[m] + I Log[4] + (I/4) (Log[4] - 1) m + ((3 I)/128) (6 Log[4] - 7) m^2 + \[Ellipsis]) + (Sqrt[1 - z^2]/Sqrt[z^2 - 1]) (ArcTanh[z] + (1/4) (z/(z^2 - 1) + ArcTanh[z]) m + (3/64) ((z (5 z^2 - 3))/(z^2 - 1)^2 + 3 ArcTanh[z]) m^2 + \[Ellipsis]) /; (m -> 0)










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> m </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiND", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox["m", "4"], "+", FractionBox[RowBox[List["9", " ", SuperscriptBox["m", "2"]]], "64"], "+", "\[Ellipsis]"]], ")"]], " ", RowBox[List["Log", "[", "m", "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", "4", "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "4", "]"]], "-", "1"]], ")"]], " ", "m"]], "+", RowBox[List[FractionBox["1", "128"], " ", RowBox[List["(", RowBox[List["3", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", RowBox[List["Log", "[", "4", "]"]]]], "-", "7"]], ")"]], " ", SuperscriptBox["m", "2"]]], "+", "\[Ellipsis]"]], ")"]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[FractionBox["z", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "+", RowBox[List["ArcTanh", "[", "z", "]"]]]], ")"]], " ", "m"]], "+", RowBox[List[FractionBox["3", "64"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["z", "2"]]], "-", "3"]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "2"]], "+", RowBox[List["3", " ", RowBox[List["ArcTanh", "[", "z", "]"]]]]]], ")"]], " ", SuperscriptBox["m", "2"]]], "+", "\[Ellipsis]"]], ")"]]]], SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]], "/;", RowBox[List["(", RowBox[List["m", "\[Rule]", "0"]], ")"]]]]]]]]










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





2001-10-29





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